DESH: overhead reduction algorithms for deferrable scheduling

Transcription

1 DOI /s DESH: overhead reduction algorithms for deferrable scheduling Ming Xiong Song Han Deji Chen Kam-Yiu Lam Shan Feng Springer Science+Business Media, LLC 2009 Abstract Although the deferrable scheduling algorithm for fixed priority transactions (DS-FP) has been shown to be a very effective approach for minimizing realtime update transaction workload, it suffers from its on-line scheduling overhead. In this work, we propose two extensions of DS-FP to minimize the on-line scheduling overhead. The proposed algorithms produce a hyperperiod from DS-FP so that the schedule generated by repeating the hyperperiod infinitely satisfies the temporal validity constraint of the real-time data. The first algorithm, named DEferrable Scheduling with Hyperperiod by Schedule Construction (DESH-SC), searches the DS-FP schedule for a hyperperiod. The second algorithm, named DEferrable Scheduling with Hyperperiod by Schedule Adjustment (DESH-SA), adjusts the DS-FP schedule M. Xiong Bell Labs, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill, NJ 08807, USA xiong@research.bell-labs.com S. Han ( ) Department of Computer Sciences, University of Texas at Austin, 1 University Station C0500, Taylor Hall 2.124, Austin, TX , USA shan@cs.utexas.edu D. Chen Emerson Process Management, Research Blvd # 3, Austin, TX , USA Deji.Chen@EmersonProcess.com K.-Y. Lam Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong cskylam@cityu.edu.hk S. Feng The Mathematics and Software Science College, Sichuan Normal University, Chengdu, Sichuan, China fengs@sicnu.edu.cn

2 in an interval to form a hyperperiod. Our experimental results demonstrate that while both DESH-SC and DESH-SA can reduce the scheduling overhead of DS-FP, DESH- SA outperforms DESH-SC by accommodating significantly more update transactions in the system. Moreover, DESH-SA can also achieve near-optimal update workload. Keywords Real-Time databases Temporal validity constraint Fixed priority scheduling Deferrable scheduling 1 Introduction Real-time embedded systems are important components of many time-critical applications that require timely processing of massive amount of real-time data. The correct functioning of a real-time embedded system depends not only on meeting real-time constraints of application jobs, but also on the accuracy of real-time data values sampled from real-world entities. Examples of real-time data include sensor data in sensor networks, positions of aircrafts in air traffic control systems, and vehicle velocity in adaptive cruise control applications. To provide better management of sampled real-time data and to support effective processing of application jobs, realtime data are typically managed by a real-time database system (RTDBS). passage of time since the status of the corresponding entity in the real-world may change continuously. Sensor update transactions should constantly sample real-world data values and install them into the RTDBS. One efficient way to determine the correctness of real-time data in a RTDBS is to define a validity constraint (Song and Liu 1995; Ramamritham 1993; Kuo and Mok 1992, 1993; Hoetal.1997; Gerber et al. 1994; Xiong et al. 2002, 2005; Kang et al. 2002; Lam et al. 2004; Gustafsson and Hansson 2004a, 2004b; Chen and Mok 2004; Xiong and Ramamritham 2004) orage constraint (Burns and Davis 1996), which determines a validity interval length for each real-time data object. A real-time data value is only valid within its validity interval. In practice, for safety and reliability reasons, real-time embedded systems require continuous generation of update transactions to refresh real-time data objects regardless of how much the status of the corresponding real-world entities have been changed. To meet this constraint, it is important to produce a schedule for all update transactions such that for any consecutive updates of a real-time data object, the next update is completed before the previous validity interval expires. Thus one of the crucial issues in the design of realtime embedded systems is to schedule the update transactions efficiently to maintain the validity of real-time data while minimizing the total update transaction workload. Prior work Most of the previous work in update transaction scheduling assumed a periodic transaction model. The update problem for periodic update transactions consists of two parts (Xiong and Ramamritham 2004): (1) the determination of the sampling periods and deadlines of update transactions; and (2) the scheduling of update transactions. One of the proposed approaches is the Half-Half (HH) scheme (Ramamritham 1993; Hoetal.1997) in which an update transaction has a fixed period that is half of the validity interval. If the set of transactions is schedulable

3 in HH, the validity constraints of the corresponding real-time data objects can also be guaranteed. Similarly to HH, More-Less (ML) (Xiong and Ramamritham 2004; Lam et al. 2004; Chen and Mok 2004) is another periodic approach in which update transactions are scheduled based on the deadline monotonic algorithm (Leung and Whitehead 1982). Compared to HH, ML can guarantee the validity of real-time data objects with less update transaction workload. Recently, the DS-FP algorithm was proposed (Xiong et al. 2005) to further reduce the total update transaction workload. The main idea of DS-FP is to adopt sporadic task model instead of the periodic model. Compared to ML, DS-FP increases the separation of two consecutive transaction jobs by releasing an update transaction job as late as possible based on the sampling time of its previous job. Both theoretical analysis and experimental results have demonstrated that DS-FP outperforms HH and ML significantly in reducing the update transaction workload while still maintaining the real-time data validity. One major problem of DS-FP is its time complexity for on-line schedule computation (Xiong et al. 2005). The variation in its run-time overhead leads to unpredictability of the system performance. This paper thus aims at reducing the on-line scheduling overhead of the DS-FP algorithm to constant, which provides more predictability to the system performance. We propose two Deferrable Scheduling with Hyperperiod (DESH) algorithms, which construct the hyperperiod schedule off-line and reduce the on-line scheduling time complexity to O(1). Contributions The key contributions of our work include the followings. (1) To reduce on-line scheduling overhead, our first algorithm, named Deferrable Scheduling with Hyperperiod Construction (DESH-SC), searches the hyperperiod of the set of update transactions so that the transactions can be scheduled by repeating the hyperperiod schedule. However, the hyperperiods found by DESH- SC are exponentially long, which could incur significant space overhead for maintaining the hyperperiod information for on-line scheduling. (2) Our second algorithm, named Deferrable Scheduling with Schedule Adjustment (DESH-SA), adjusts the DS-FP schedule in an interval such that the adjusted schedule can be repeated infinitely. DESH-SA improves DESH-SC on producing much shorter hyperperiods and accommodating significantly more update transactions. (3) The two DESH algorithms are experimentally studied by simulation, and the primary performance metrics used in our experimental studies are the CPU workload and the number of transactions supported in the system. Our experimental results demonstrate that both DESH-SC and DESH-SA can reduce scheduling overhead of DS-FP, and DESH-SA outperforms DESH-SC by accommodating significantly more update transactions in the system. Organization This paper is organized as follows: Sect. 2 briefly reviews the background and related work in the area. Section 3 presents the details of the two proposed algorithms. Section 4 reports our experimental results of DESH-SC and DESH-SA. Finally, we conclude the paper and discuss the future work in Sect. 5.

4 2 Background and related work This section briefly reviews the temporal validity of real-time data, and the More- Less (ML) (Burns and Davis 1996; Xiong and Ramamritham 2004) and deferrable scheduling (DS-FP) (Xiong et al. 2005) algorithms. Formal definitions of the frequently used symbols are summarized in Table 1. Definition 2.1 A real-time data object (X i ) at time t is temporally valid (or absolutely consistent) if, for its jth update finished latest before t, the sampling time (r i,j )plusthevalidity interval (V i ) of the data object is not less than t, i.e., r i,j + V i t (Ramamritham 1993). A data value for real-time data object X i sampled at any time t will be valid up to (t + V i ). The actual length of the temporal validity interval of a real-time data object is application dependent (Ramamritham 1993, 1996; Locke 1997). One of the important design goals of RTDBS is to guarantee that real-time data remain fresh, i.e., they are always valid. We assume that the network delay for a sensor update transaction job to be sent from a sensor to the RTDBS (i.e., jitter between sampling time at the sensor and release time at the RTDBS) is zero for convenience of presentation. Our results here can be easily extended to the case that jitter is non-zero if the maximum jitter of a transaction is known. In the presence of non-zero jitters, we can transform a transaction τ i (with validity length V i and maximum jitter δ i) to a transaction τ i (with validity length V i = V i δ i and zero jitter). Such a transformation guarantees that if τ i can meet its validity constraint, then τ i can also meet its validity constraint. Given a set of transactions T ={τ i } m i=1, we assume without loss of generality that τ k has higher priority than τ j for k<j. Table 1 Symbols and definitions Symbol Definition X i Real-time data object i τ i Update transaction updating X i (i = 1,...,m) J i,j The jth job of τ i (j = 0, 1, 2,...) R i,j Response time of J i,j C i V i f i,j r i,j d i,j P i D i U DS i (a, b) Computation time of transaction τ i Validity (interval) length of X i Finishing time of J i,j Release (Sampling) time of J i,j Absolute deadline of J i,j Period of transaction τ i in ML Relative deadline of transaction τ i in ML An estimated average CPU utilization in DS-FP Total cumulative processor demands from higherpriority transactions received by τ i in interval [a,b)

5 More-less ML adopts the periodic task model (Leung and Whitehead 1982) for sensor update transactions whose derived deadlines are not larger than their periods. Consider synchronous transactions whose first jobs all start at time 0. A time instant after which a transaction job has the worst-case response time is called a critical instant, e.g., time 0 is a critical instant for all the transactions with deadlines no larger than their periods if those transactions are synchronous (Leung and Whitehead 1982). Note that we only consider synchronous transactions. In ML, there are three constraints to follow for transactions τ i ( i, 1 i m) (Xiong and Ramamritham 2004): Validity constraint: the sum of the period and relative deadline of transaction τ i is always less than or equal to V i, i.e., P i + D i V i. Deadline constraint: the period of an update transaction is assigned to be more than or equal to half of the validity length of its updated object, while its corresponding relative deadline is less than or equal to half of the validity length of the same object. For τ i to be schedulable, D i must be greater than or equal to C i,theworstcase execution time of τ i, i.e., C i D i <P i. Schedulability constraint: for a given set of update transactions, the Deadline Monotonic scheduling algorithm (Leung and Whitehead 1982) is used to schedule the transactions. That is, i j=1 ( D i P j C j ) D i (1 i m). ML assigns priorities to transactions based on Shortest Validity First (SVF), i.e., in the inverse order of validity length, and ties are resolved in favor of transactions with larger computation time (C i ). It assigns deadlines and periods to τ i as follows: D i = fi,0 ml i,0, (1) P i = V i D i, (2) where fi,0 ml and rml i,0 are the finishing and sampling times of the first job of τ i, respectively. Note that in a synchronous system, ri,0 ml = 0 and the first job s response time is the worst-case response time in ML. We use superscript ml to distinguish the finishing and sampling times in ML from those in DS-FP. DS-FP ML is pessimistic on the deadline and period assignment. This is because it uses a periodic task model that has a fixed period and relative deadline for each transaction, and the relative deadline D i is equal to the worst-case response time of the transaction. According to the validity constraint in ML, the larger the deadline D i, the smaller the period P i. In order to increase the separation of two consecutive jobs (and thus reduce the sensor update workload), DS-FP adaptively derives the relative deadline and separation of one job from its previous job and preemptions from higherpriority transactions. Given release time r i,j of job J i,j and deadline d i,j+1 of job J i,j+1 (j 0), d i,j+1 = r i,j + V i (3) guarantees that the validity constraint can be satisfied, as depicted in Fig. 1. Correspondingly, the following equation follows directly from (3): (r i,j+1 r i,j ) + (d i,j+1 r i,j+1 ) = V i. (4)

6 Fig. 1 Illustration of DS-FP scheduling If r i,j+1 can be shifted onward to r i,j+1 along the time line in Fig. 1, it does not violate (4). After the shift, temporal validity can still be guaranteed as long as J i,j+1 is completed by its deadline d i,j+1. The idea of DS-FP is to defer the sampling time (i.e., release time), r i,j+1,ofj i,j s next job as late as possible while still guaranteeing the validity constraint. According to the fixed priority scheduling theory, r i,j+1 in DS-FP can be derived backwards from its deadline d i,j+1 as follows: r i,j+1 = d i,j+1 R i,j+1 (r i,j+1,d i,j+1 ); (5) R i,j+1 (r i,j+1,d i,j+1 ) = i (r i,j+1,d i,j+1 ) + C i. (6) where i (a, b) denotes the total cumulative processor demands made by all jobs of higher-priority transaction τ k ( k, 1 k i 1) during time interval [a,b), and R i,j+1 (r i,j+1,d i,j+1 ) (or R i,j+1 for simplicity in DS-FP) the response time of J i,j+1 deriving backwards from its deadline d i,j+1. Note that the schedule of all higherpriority jobs that are released prior to d i,j+1 needs to be computed before computing i (r i,j+1,d i,j+1 ). Similarly to ML, DS-FP also assigns priorities to transactions according to SVF. Readers are referred to the Appendix for the details of the DS-FP algorithm. Now we summarize the algorithm as follows. First we set r i,0 = 0, i, 1 i m. The highest priority job among the outstanding jobs is always scheduled first. It is only preempted when a new job with higher priority is ready. As soon as a job J i,j is completed, we derive the r i,j+1 of its next job according to above calculations. The algorithm fails when a job misses its deadline. Otherwise it keeps running. It is proved that any task set that is scheduled by ML is also scheduled by DS-FP (Xiong et al. 2006). The EDL algorithm proposed in Chetto and Chetto (1989) processes tasks as late as possible based on the Earliest Deadline algorithm (Liu and Layland 1973). EDL assumes that all deadlines of tasks are given whereas DS-FP and DESH algorithms

7 derive deadlines dynamically. The validity constrained scheduling, e.g., ML, DS-FP, and DESH algorithms, are different from the distance constrained scheduling, which guarantees an upper bound to the finishing times of two consecutive instances of a task (Han et al. 1995). 3 Deferrable scheduling with hyperperiod The DS-FP algorithm is very effective at reducing processor utilization while guaranteeing the validity constraint. However, its on-line scheduling overhead in terms of time complexity is much higher than that of ML. Moreover, the scheduling overhead of DS-FP depends on the number of transactions and the validity length of updated data. Thus, DS-FP can become very expensive, e.g., when the transaction set becomes large. In contrast to a periodic schedule that has the least common multiple of task periods as its hyperperiod, there is usually no such natural hyperperiod for a DS-FP schedule. Next, we present two DEferrable Scheduling with Hyperperiod (DESH) algorithms for constructing periodic schedules off-line from the DS-FP algorithm so that the on-line scheduling time complexity can be reduced. Note that this will undoubtedly increase the space overhead for keeping the DESH schedules. But the space overhead can be kept reasonably low as demonstrated in our experiments in Sect. 4.OurDESH algorithms satisfy the following properties: Property 3.1 A schedule satisfies the validity constraint. Property 3.2 The on-line scheduling time complexity is O(1). 3.1 DEferrable Scheduling with Hyperperiod: Schedule Construction (DESH-SC) In this subsection, we present DEferrable Scheduling with Hyperperiod based on Schedule Construction (DESH-SC), a DS-FP based algorithm that can reduce the online scheduling overhead. The basic idea of DESH-SC is to search for an interval of DS-FP schedule, the hyperperiod, that could be repeated infinitely without violating the validity constraint. Note that DESH-SC could return without finding a hyperperiod. The DESH-SC algorithm consists of two parts: an algorithm for finding the hyperperiod off-line (see Algorithm 3.1) and an algorithm for scheduling transactions on-line. The latter is trivial once a hyperperiod is found because it only needs to repeat the hyperperiod schedule. Therefore, we next describe how the hyperperiod is derived from the schedule of DS-FP. For a DS-FP schedule and a time period [t s,t e ],wesay[t s,t e ] is a hyperperiod for the transaction set if for all transactions τ i (1 i m), the following schedule satisfies τ i s validity constraint: it is the same as the DS-FP schedule from time 0 to t e.fromt e onward, it repeats the DS-FP schedule in [t s,t e ] to infinity. Please note that t s and t e do not need to be idle time points in DESH-SA, which is different from the requirements of t s and t e in DESH-SC.

8 Lemma 3.1 [t s,t e ] is a hyperperiod in DESH-SC if for all τ i (1 i m) the following conditions hold. 1. t s and t e are CPU idle time points. 2. t s > V i. 3. τ i is scheduled at least once in [t s,t e ]. 4. I(t s,τ i ) I(t e,τ i ), where function I(t,τ i ) is defined as the time distance between t and τ i s latest release time before t. Proof Given any τ i (1 i m), we first prove in the hyperperiod schedule that the distance of the finish time of the first τ i job after t e and the release time of its latest job before t e satisfies the validity constraint. Note that the first job after t e repeats the first job in [t s,t e ]. Because t s > V i, the first job of τ i in [t s,t e ] must finish by (t s I(t s,τ i )) + V i, in other words, by V i I(t s,τ i ) after t s. Since [t s,t e ] is repeated after t e, the first job of τ i after t e also finishes by V i I(t s,τ i ) after t e. The distance between the finish time of its first job in the second hyperperiod [t e, 2t e t s ] and the release time of its latest job in the first hyperperiod [t s,t e ] is no longer than: I(t e,τ i ) + (V i I(t s,τ i )) = V i + (I (t e,τ i ) I(t s,τ i )) V i. Similarly, we can prove that the distance between the finish time of its first job in the (k + 1)th (k = 1, 2,...) hyperperiod and the release time of its latest job in the kth hyperperiod is no longer than V i. Thus, the jobs of τ i satisfy the validity constraint. Note that the third condition could be derived from the fourth condition: If no job is scheduled in [t s,t e ], then τ i s latest release time before t s is also its latest release time before t e, hence the fourth condition is always false. To better satisfy the fourth condition, we need to assign t s to be the end of an idle period and t e to be the beginning of another idle period. By idle period [t 1,t 2 ] we mean that CPU is busy right before t 1, it idles between t 1 and t 2, and it is busy again after t 2. Once the hyperperiod is found, we could increase t e as long as the conditions in Lemma 3.1 are satisfied. The idea is presented in Algorithm 3.1. In the algorithm, we continuously push t 2 of idle periods into a queue Q as possible candidates for t s of a hyperperiod. For each subsequent idle period, we check its t 1 against each t 2 saved in Q to see if they form a hyperperiod. If the hyperperiod is found, we could then further increase t e as long as [t s,t e ] still satisfies the conditions in Lemma 3.1. The increase cannot exceed I(t s,τ i ) I(t e,τ i ) for any transaction τ i, 1 i m.we define w to be the minimum of I(t s,τ i ) I(t e,τ i ) in the algorithm. Algorithm 3.1 SearchHyperperiod: Input: A DS-FP schedule, a utilization limit U max, and a time limit t max. Output: The hyperperiod with utilization U max. 1 U 1.001; // Initialization of hyperperiod utilization. 2 t 2 max{v i 1 i m}; 3 [t 1,t 2 ] first CPU idle period after t 2 ;

9 4 Append t 2 to Q; //Q is a FIFO queue of t 2. 5 while (U > U max ) do 6 [t 1,t 2 ] next CPU idle period after t 2 ; 7 // t max is the maximum time to search. 8 if (t 1 >t max ) then return failure; endif 9 t e t 1 ; 10 for t s = first in Q to last in Q do 11 if ([t s,t e ] satisfies Condition 4 in Lemma 3.1) 12 then 13 Signal that a hyperperiod exists; 14 w min{i(t s,τ i ) I(t e,τ i ) 1 i m}; 15 t e t e + min(w, (t 2 t 1 )); // Fine-tune t e. 16 U utilization in [t s,t e ]; 17 if (U > U ) then 18 U U ; 19 if (U U max ) then goto RT N; endif 20 endif 21 endif 22 end 23 if Q is full then Dequeue the oldest; endif 24 Append t 2 to Q; 25 end 26 RTN: return [t s,t e ] as the hyperperiod; Note that Algorithm 3.1 is not guaranteed to find a hyperperiod if one exists. This is due to the time limit (t max ), space limit (the size of Q), and the value of U max.the value of U max should not exceed 1.0. In our experiments, U max is set as a value close to the average utilization estimation of DS-FP defined in Definition 3.1 (Sect. 3.2). The following example demonstrates how the algorithm works. Example 3.1 Suppose that there are three update transactions whose parameters are shownintable2. The resulting periods and deadlines in ML are shown in the same table. For each job of τ 1, τ 2 and τ 3 before time 45, Table 3 compares its (release time, deadline) pairs which are assigned by ML and DS-FP respectively. Figure 2(a) depicts part of a DS-FP schedule during the interval [15, 45], where t1 i and ti 2 are the beginning and ending times of the ith (i = 1, 2,...) idle period respectively. In the DS-FP schedule, the first idle period after V 3 = 20, i.e., the largest V i,is[21, 22]. Table 2 Parameters derived from ML τ 1 τ 2 τ 3 C i V i P i D i 1 3 6

10 Table 3 Release time and deadline comparison Job τ 1 τ 2 τ 3 ML/DS-FP ML DS-FP ML DS-FP 0 (0,1) (0, 3) (0, 3) (0, 6) (0, 6) 1 (4,5) (7, 10) (7, 10) (14, 20) (18, 20) 2 (8,9) (14, 17) (14, 17) (28, 34) (35, 38) 3 (12,13) (21, 24) (22, 24) (16,17) (28, 31) (30, 32) 5 (20,21) (35, 38) (38, 40) 6 (24,25) (28,29) 8 (32,33) 9 (36,37) t2 1 = 22 is pushed in Q. During the next three idle periods, the condition of Line 11 in Algorithm 3.1 always fails. Note that τ 3 has not been scheduled yet since V 3. For the fifth idle period [t1 5,t5 2 ]=[41, 44], the second element in Q with t2 2 = 28 satisfies the condition of Line 11 in Algorithm 3.1.Wehavet s = 28, w = I(28,τ 1 ) I(41,τ 1 ) = 3, t e = 41 + min(w, (t 2 t 1 )) = = 44, and U = 10/16 = If U max 0.625, Algorithm 3.1 returns hyperperiod [28, 44]. Note that Algorithm 3.1 does not depend on which scheduling algorithm produces the input schedule. It could be applied to any valid schedule satisfying the validity constraint. The complete DESH-SC schedule constructed from Algorithm 3.1 satisfies the Properties 3.1 and DEferrable Scheduling with Hyperperiod: Schedule Adjustment (DESH-SA) In this subsection, we present DEferrable Scheduling with Hyperperiod based on Schedule Adjustment (DESH-SA), a DS-FP based algorithm that can reduce the online scheduling overhead while achieving processor utilization close to that of DS-FP. By schedule adjustment, we mean changing release times and deadlines of jobs. The basic idea of DESH-SA is to construct a hyperperiod schedule S H off-line for T, a set of validity constrained transactions. Suppose the first hyperperiod of the S H schedule has length S H. If the first hyperperiod of S H can be constructed by adjusting the DS-FP schedule in the time interval [0, S H ], the complete S H schedule can be constructed by repeating the first hyperperiod of S H infinitely every S H time units. Thus, similarly to DESH-SC, thedesh-sa algorithm consists of two parts: an algorithm for constructing the hyperperiod off-line (see Algorithm 3.2) and an algorithm for scheduling transactions on-line. We next describe how the first hyperperiod schedule of S H in the interval [0, S H ] is derived from the schedule of DS-FP. Given time t e > 0, note that a DS-FP schedule in the interval [0,t e ] can be constructed off-line. Assume that jobs J i,ki 1 and J i,ki of τ i (k i 1&1 i m) satisfy

11 Fig. 2 DESH-SC and DESH-SA examples the following condition for t e : d i,ki 1 <t e d i,ki. (7) First, deadlines d i,ki will be adjusted to time t e if they are different, i.e., all jobs J i,ki ( i, 1 i m) must complete by t e. Note that there are J i,0,...,j i,ki, i.e., k i +1 jobs of τ i, during the interval [0,t e ] after the adjustment, and k i is the largest index of all jobs of τ i that complete by t e. Likewise, let jobs J i,ki +1 ( i, 1 i m) of all τ i safter adjustment be released from time t e, which is similar to the case that the first jobs are all released from time 0. Thus, jobs of all transactions can be released synchronously at time nt e, where n is a natural number. This can be done by repeating schedule in [0,t e ] forever. Second, let the DS-FP schedule in [0,t e ] be adjusted backwards from time t e so that the adjusted schedule is valid for guaranteeing the validity constraint. Thefollowing condition can be enforced for 0 t t e and integers n 1,n 2 0 if the schedule in the interval [0,t e ] is repeated infinitely: g(n 1 t e,t)= g(n 2 t e,t) (8) where g(nt e,t) is a function returning a pair of integers i, k, which indicates that the kth job of τ i in the nth hyperperiod is active at time t (i.e., at time nt e + t). Equa-

12 tion (8) implies that any two hyperperiods have the exactly same schedule. Function g(nt e,t)is formally defined as i, j n(k i + 1), the CPU is allocated to J i,j g(nt e,t)= at time nt e + t; (9) 0, 0, the CPU is idle at time nt e + t. Note that n, j are integers, and n 0&j 0 hold for (9). Equation (8) ensures that all transactions are released synchronously at time 0, t e,2t e,..., etc. If the processor is allocated to job J i,j at time nt e + t, then it is the (j n(k i + 1))th job of τ i from time nt e (Note that there are (k i + 1)τ i jobs during the interval [0,t e ]). Equations (8) and (9) ensure that the complete S H schedule is constructed periodically by repeating the schedule of the interval [0,t e ] every t e units. Next, we present an estimation of the average processor utilization of DS-FP, U DS, from a statistical perspective and discuss how time t e is chosen. Definition 3.1 Given a set of transactions T ={τ i } m i=1 that can be scheduled by ML, let P j be the average period for τ j, the estimated average processor utilization under DS-FP, U DS is defined as follows: U DS = m i=1 C i P i = m ( i=1 V i C i C i 1 i 1 C j j=1 P j First, t e has to be a value that allows the processor utilization of the first S H hyperperiod to be close to U DS, which is demonstrated to be very close to the average utilization of fixed priority transactions with the same priority assignment (Xiong et al. 2005). Any time t 0 can be chosen as the initial value of t e if the processor utilization at t e, U(t e ) is close to U DS, where U(t e ) is defined as follows: mi=1 (k i + 1)C i U(t e ) =. (11) t e Please note that k i is the index of the last job (i.e., J ki ) of transaction τ i that completes by time t e. Second, t e can be chosen from an idle time. The following theorem, which is a sufficient condition of constructing a general DESH-SA schedule for a validity constrained transaction set without any adjustment, explains the rationale for choosing an idle time as t e. Theorem 3.1 Given a DS-FP schedule for a validity constrained transaction set T, suppose t idle is an idle time in the schedule and the schedule before t idle is feasible. Let r i,ki 1 (k i 1) be the latest release time of jobs of τ i (1 i m) before t idle. If ) (10)

13 i (1 i m), t idle r i,ki 1 + d i,0 V i (12) holds, then the interval [0,t idle ] can be used as the first hyperperiod of the DESH-SA schedule without any adjustment. Proof Note that once a job is released under DS-FP, the processor cannot be idle until the job completes. Thus, i (1 i m), d i,ki 1 <t idle <r i,ki (13) If all jobs J i,ki are released at time t idle, i.e., r i,ki = t idle, then the schedule of the interval [t idle, 2 t idle ] is the same as that of the interval [0,t idle ]. Moreover, if (12) holds, d i,ki r i,ki 1 = d i,ki t idle + t idle r i,ki 1 = d i,0 0 + t idle r i,ki 1 V i {by (12)} That is, two consecutive jobs J i,ki 1, J i,ki ( i, 1 i m) across two neighboring hyperperiods satisfy the validity constraint. Thus a feasible DESH-SA schedule can be constructed by having the schedule of the interval [0,t idle ] as the first hyperperiod schedule. Note that if t e is set to be t idle, then it is not necessary to adjust the schedule of any transactions in the interval [0,t idle ] for making the first hyperperiod of DESH-SA. However, it is not always possible to find such a time t idle for all transactions satisfying (12), in which case the DS-FP schedule in the interval [0,t e ] corresponding to a subset of the transactions needs to be adjusted. Specifically, if transaction τ h (1 h m) is the highest priority transaction whose schedule needs to be adjusted due to violation of (12), then the schedule of all lower-priority transactions τ i (h < i m) also needs to be adjusted due to the impact of release time and deadline adjustment of τ i s higher-priority transactions in the interval [0,t e ]. This is described in Algorithm 3.2. Algorithm 3.2 AdjustScheduleForHyperperiod(T, t e ): Input: Transaction set T and time t e > 0. Output: Adjusted schedule S H in [0,t e ] satisfying (8), and i, k i. 1 Construct DS-FP schedule S H in [0,t e ] for τ i T ; 2 //J i,j has r i,j,d i,j computed in S H (j k i by (7)). 3 h min i {i τ i T & τ i violates (12)}. 4 //J i,ki is the latest τ i job in the interval [0,t e ]. 5 (i < h), k i k i 1; // No adjustment for i<h

14 6 t s t e ; // Schedule in [t s,t e ] will be adjusted. 7 for i = h to m do // Adjust S H in [0,t e ]. 8 d i,k i t e ; // d i,j is adjusted from d i,j. 9 j k i ; 10 while (j > 0) do 11 if (d i,j r i,j < i (r i,j,d i,j ) + C i) 12 // J i,j s response time >d i,j r i,j. 13 then // r i,j is adjusted from r i,j. 14 r i,j d i,j i(r i,j,d i,j ) C i; 15 if (((j < k i ) (d i,j+1 r i,j > V i)) (r i,j < 0)) 16 then report failure; endif 17 if (r i,j <d i,j 1) // Ripple impact. 18 then d i,j 1 r i,j ; // Change d i,j else d i,j 1 d i,j 1; // No change. 20 endif 21 j j 1; 22 else // No adjustment for this job. 23 if (t s d i,j ) // No more adjustment for τ i. 24 then 25 t s = d i,j ; 26 break; // Jump out of while loop 27 else // Examine the previous job of τ i. 28 d i,j 1 d i,j 1; // No change. 29 j j 1; 30 endif 31 endif 32 end 33 if ((j = 0) ((d i,j < i(0,d i,j ) + C i))) 34 then report failure; 35 else t s 0; 36 endif 37 end 38 return adjusted S H in [0,t e ] and i, k i ; Note that Line 11 checks if J i,j s response time is greater than d i,j r i,j,the difference of its adjusted deadline and original release time. If so, its release time also needs to be adjusted backwards. This may cause a violation of the validity constraint, thusdesh-sa reports failure (Line 16). Otherwise, if itsnewlyadjusted release time is ahead of its prior job s deadline, then its prior job s schedule has to be adjusted. This causes a ripple impact on the schedule adjustment. The next example illustrates DESH-SA. Example 3.2 Figure 2(b) shows the result of applying DESH-SA on the same transaction set as in Example 3.1. The upper and lower schedules in Fig. 2(b) are the DS-FP

15 and its corresponding DESH-SA schedules, respectively. Let t e = 33, then h = 3. Only τ 3 needs to be adjusted. DESH-SA sets d 3,1 = 33. J 3,1 can be re-scheduled and its adjusted release time is 27. The newly adjusted schedule from time 0 to 33 is the DESH-SA hyperperiod. Theorem 3.2 Given a synchronous update transaction set T with known C i and V i (1 i m), if ( i) fi,0 ml V i 2 in ML, then WCRT i f ml i,0 where WCRT i and f ml i,0 denote the worst-case response time of τ i under DS-FP and ML, respectively. Proof See Theorem 3.1 in Xiong et al. (2008). After the schedule adjustment, the release time and deadline of job J i,ki +1 ( i, 1 i m), which appears as the first job in the second hyperperiod, are set as follows: r i,k i +1 = t e; (14) d i,k i +1 = t e + d i,0. (15) Lemma 3.2 If fi,0 ml V i 2 in ML, the release time of J i,k i and the deadline of J i,ki +1 after adjustment in Algorithm 3.2 is constrained by V i, i.e., d i,k i +1 r i,k i V i. (16) Proof i (i<h), (k i 1) is assigned to k i at Line 5 in Algorithm 3.2. By Theorem 3.1, t e + d i,0 r i,ki V i d i,k i +1 r i,k i V i {by Algorithm 3.2, r i,k i = r i,ki } Next, we prove it for h i m. By schedule adjustment, r i,k i +1 = d i,k i = t e. (17) After the schedule adjustment, according to Theorem 3.2, the following equations hold: The sum of (18) and (19) is: d i,k i +1 r i,k i +1 f i,0 ml (18) d i,k i r i,k i fi,0 ml (19) d i,k i +1 r i,k i 2f ml i,0 V i. Thus, (16) holds.

16 Lemma 3.2 guarantees that the validity constraint can be satisfied for J i,ki and J i,ki +1, which are two consecutive jobs in different hyperperiods (e.g., the 1st and 2nd hyperperiods). Algorithm 3.2 also guarantees that the validity constraint can be satisfied for jobs J i,0,..., J i,ki, which are in the same hyperperiod. Moreover, if the schedule of the first S H hyperperiod can be constructed off-line, the on-line scheduling overhead of DESH-SA in terms of time complexity is constant as it only needs to repeat the schedule of the first S H hyperperiod infinitely. Therefore, the complete DESH-SA schedule constructed from Algorithm 3.2 satisfies the aforementioned Properties 3.1 and Performance evaluation This section presents important results from our simulation studies of the DESH algorithms. Our goal is to find out whether the DESH algorithms are effective for reducing the DS-FP overhead. The primary performance metrics used in our experimental studies are the CPU workload and the number of transactions supported in the system. 4.1 Simulation model and parameters In the experiments, we investigate whether DESH-SA and DESH-SC can find a hyperperiod, and if so, how much excess CPU workloads they may incur compared to DS-FP. We also compare the hyperperiod length of DESH-SA and DESH-SC to study the space efficiency of the approaches, and demonstrate the percentage of transactions to be adjusted when we calculate the hyperperiod for DESH-SA. For simplicity, only one version of a real-time data object is maintained. Upon refreshing a real-time data object, the older version is discarded. We ignore the on-line scheduling overhead in our experiments, and consider it to be O(1) for all algorithms (which is true for DESH algorithms). This is in favor of DS-FP as its scheduling overhead is ignored for the CPU workload in our experiments. We define N adjust to be the average number of jobs whose release times or deadlines are adjusted in [0,t e ] under DESH-SA. A summary of the parameters and default settings is presented in Table 4. The baseline values for the parameters follow those used in Xiong and Ramamritham (2004), which are originally from air traffic control applications. Two categories of parameters are defined: system and update transaction parameters. For system configurations, we only consider a single CPU, main memory based RTDBS. The number Table 4 Parameters and default settings Parameter Meaning Value N CPU No. of CPU 1 N T No. of real-time data [10, 300] V i (ms) Validity interval of X i [4000, 8000] C i (ms) Time for updating X i [5, 15] Trans. length No. of data to update 1

17 of real-time data varies from 10 to 300 and the validity length of each real-time data object is uniformly distributed from 4000 to 8000 ms. For update transactions, it is assumed that each transaction updates one real-time data object, and its CPU time is uniformly distributed from 5 to 15 ms. 4.2 Experimental results In this subsection, the CPU workloads of sensor update transactions produced by DS-FP, DESH-SC and DESH-SA are quantitatively compared. In the first set of experiments, update transactions are generated randomly according to the parameter settings in Table 4 while in the second set of experiments, m i=1 C i V i of the update transaction set is fixed at 45% and V i C i is varied to show its impact on the performance of the algorithms. With the DESH algorithms, the transaction with maximum validity interval is run at least 200 times (thus issuing 200 jobs) so that the CPU workload of the first S H hyperperiod is close to U DS. Then the idle times following the completion of those jobs under DS-FP are chosen as t e candidates. Those candidates are tested to find out whether the interval [0,t e ] can be used as the first hyperperiod. The resulting CPU workloads generated from DESH-SA, DESH-SC and DS-FP are depicted in Fig. 3. In the figure, DS-FP(Est.) indicates the estimated average CPU utilization U DS, and DS-FP(Expt.) is the actual utilization of DS-FP obtained in the experiments. The results in Fig. 3 demonstrate that the CPU workload of DS-FP(Est.) nearly matches that of DS-FP(Expt.). In Fig. 3, thedesh-sc curve is only plotted in the range where the number of update transactions in the system varies from 5 to 35. This is because in our experiments, DESH-SC can only find its hyperperiod when the number of update transactions is no more than 35. Indeed, CPU workloads of DESH-SC and DESH-SA nearly match that of DS-FP, and it is hard to tell the difference in the figure. However, it is observed that the DESH-SA workload is consistently lower than that of ML. This is expected because the deadline adjustment in DESH-SA has little impact on increasing the overall system workload. Even when the number of transactions in the system is up to 300, DESH-SA only incurs less than 1% Fig. 3 CPU workload comparison

18 Fig. 4 Average # of adjusted jobs per transaction in [0,t e ] Fig. 5 Average hyperperiod length comparison excess CPU workload compared to that of DS-FP. Note that the on-line scheduling overhead is ignored for DS-FP in our experiments. Thus the actual CPU workload for DS-FP should be higher than what is shown in the figure. Also note that the extra overhead resulting from DESH-SA is adjustable. For example, if the interval [0,t e ] is further enlarged, the CPU workload of DESH-SA can be reduced, in which case it can become even closer to that of DS-FP. Figure 4 shows the average number of adjusted jobs (N adjust ) obtained for each transaction in DESH-SA. The data is collected from 50 different transaction sets. It should be noted that the average number of adjusted jobs for each transaction is lower than 2, and it increases while the priority of a transaction decreases. Considering that such job adjustment produces a hyperperiod schedule that reduces on-line scheduling overhead to O(1), the benefit of the adjustment is justified. Next, we compare the hyperperiod length calculated from DESH-SC and DESH- SA. Figure 5 shows that the hyperperiod length for DESH-SA remains almost the same with the increase of the number of transactions in the system. But the hyperperiod length for DESH-SC increases rapidly and when the number of transactions

19 Fig. 6 Hyperperiod length vs. U max (DESH-SC) Fig. 7 Percentage of transactions adjusted (DESH-SA) in the system increases beyond 35, DESH-SC cannot find a hyperperiod. A shorter hyperperiod implies that less space overhead is needed for keeping scheduling information. This implies that DESH-SA is also space efficient. We also study the impact of U max, the hyperperiod utilization limit in DESH-SC (Algorithm 3.1), on the resulting hyperperiod length. Figure 6 shows the relationship of the resulting hyperperiod length and U max. In the figure, U max is varied as 1.02 DS-FP(Est.), 1.06 DS-FP(Est.), and 1.10 DS-FP(Est.). The differences among the hyperperiod lengths are really small. A larger U max results in a slightly shorter hyperperiod because DESH-SC terminates sooner with larger U max in Algorithm 3.1. Figure 7 shows the percentage of transactions adjusted for DESH-SA. There are two percentage curves in the figure. The higher one is the percentage of transactions adjusted no matter whether they violate (12). Those transactions include all τ i where h i m (h is calculated at Line 3 in Algorithm 3.2). The lower curve is the percentage of transactions which actually violate (12). The former should be higher than the latter because if the schedule of a transaction, e.g., τ h, is adjusted, then the schedule

20 Fig. 8 CPU workload with fixed m i=1 C i V i of its lower-priority transactions will be adjusted even if a lower-priority one does not violate (12) before τ h s adjustment. As mentioned earlier, we also conducted experiments by varying V i C i and fixing mi=1 C i V i of the update transaction set at 45%. The results are depicted in Fig. 8, which compares ML, DS-FP, DESH-SA, m C i i=1 V i and m C i i=1 V i C i.asinfig.3,the actual utilization for DS-FP is very close to the estimated average utilization U DS C i V i C i (shown as DS-FP(Est.)). As explained in Xiong et al. (2005), m i=1 is the CPU workload resulting from the possible maximum separation V i C i satisfying the validity constraint for each transaction τ i. It is the CPU lower bound ignoring transaction interference. It is observed in Fig. 8 that the CPU workloads of DS-FP and DESH-SA are very close to that of m C i i=1 V i C i. The larger V i C i is, the closer DS-FP, DESH-SA and m C i i=1 V i C i are. This is because the probability of transaction interference decreases for DS-FP and DESH-SA when V i becomes larger. In summary, it is demonstrated in our experimental results that the CPU workloads produced by the DESH algorithms nearly match those produced by DS-FP. In addition, DESH-SA outperforms DESH-SC in terms of time and space complexity. Thus, DESH-SA is a very efficient algorithm for reducing the DS-FP overhead. C i 5 Conclusions and future work This paper presents novel approaches derived from DS-FP, named DESH-SC and DESH-SA, that reduce the on-line scheduling overhead to O(1). DESH-SC searches for a hyperperiod in the DS-FP schedule while DESH-SA adjusts the DS-FP schedule in an interval to satisfy the temporal validity constraint. Our experimental results demonstrate that DESH-SA is a very effective approach for minimizing the sensor update workload while guaranteeing the validity constraint, and it is efficient in terms of time and space complexity. However, there are many open questions regarding the hyperperiod in a DS-FP schedule. For example, it is unclear what a necessary and sufficient condition is for

21 the DESH-SA algorithm to produce a hyperperiod. Also, if a transaction set is not schedulable by DS-FP, is it possible to construct a hyperperiod schedule so that its constructed schedule is schedulable? We intend to address these challenging problems in our future work. Appendix: Deferrable scheduling algorithm This appendix presents DS-FP,afixed priority scheduling algorithm, which was originally presented in Xiong et al. (2005). Transaction priority assignment policy in DS- FP is the same as in ML, i.e., Shortest Validity First. Given an update transaction set T, it is assumed that τ i has a priority higher than τ j if i<j as we let V i V j. Algorithm 6.1 presents the DS-FP algorithm. There are two cases for the DS-FP algorithm: 1) At system initialization time, Lines 13 to 22 iteratively calculate the first job s response time for τ i. The first job s deadline is set as its response time (Line 23). 2) Upon completion of τ i s job J i,k (1 i m, k 0), the deadline of its next job (J i,k+1 ), d i,k+1, is derived at Line 28 so that the farthest distance of J i,k s sampling time and J i,k+1 s finishing time is bounded by the validity length V i (3). Finally, the sampling time of J i,k+1, r i,k+1, is derived backwards from its deadline by accounting for the interferences from higher-priority transactions (Line 30). Algorithm 6.1 DS-FP algorithm: Input: A set of update transactions T ={τ i } m i=1 (m 1) with known {C i} m i=1 and {V i } m i=1. Output: Construct a partial schedule S if T is feasible; otherwise, reject. 1 case (system initialization time): 2 t 0; // Initialization 3 // LSD i Latest Scheduled Deadline of τ i s jobs. 4 LSD i 0, i (1 i m); 5 l i 0, i (1 i m); 6 // l i is the latest scheduled job of τ i 7 for i = 1 to m do 8 // Schedule finish time for τ i,0. 9 r i,0 0; 10 f i,0 C i ; 11 // Calculate higher-priority (HP) preemptions. 12 oldhppreempt 0; // initial HP preemptions 13 hppreempt CalcHPPreempt(i, 0, 0,f i,0 ); 14 while (hppreempt > oldhppreempt) do 15 // Accounting for the interferences of HP tasks 16 f i,0 r i,0 + hppreempt + C i ; 17 // If this condition is violated, it is not possible to schedule two jobs 18 by V i.

22 19 if (f i,0 > V i C i ) then abort endif; 20 oldhppreempt hppreempt; 21 hppreempt CalcHPPreempt(i, 0, 0,f i,0 ); 22 end 23 d i,0 f i,0 ; 24 end 25 return; 26 case (upon completion of J i,k ) : 27 // Schedule release time for J i,k d i,k+1 r i,k + V i ; // get next deadline for J i,k+1 29 // r i,k+1 is also the sampling time for J i,k+1 30 r i,k+1 ScheduleRT(i, k + 1,C i,d i,k+1 ); 31 return; Algorithm 6.2 ScheduleRT(i, k, C i, d i,k ): Input: J i,k with C i and d i,k. Output: r i,k. 1 oldhppreempt 0; // initial HP preemptions 2 hppreempt 0; 3 r i,k d i,k C i ; 4 // Calculate HP preemptions backwards from d i,k. 5 hppreempt CalcHPPreempt(i,k,r i,k,d i,k ); 6 while (hppreempt > oldhppreempt) do 7 // Accounting for the interferences of HP tasks 8 r i,k d i,k hppreempt C i ; 9 if (r i,k <d i,k 1 ) then abort endif; 10 oldhppreempt hppreempt; 11 hppreempt GetHPPreempt(i,k,r i,k,d i,k ); 12 end 13 return r i,k ; Algorithm 6.3 CalcHPPreempt(i, k, t 1, t 2 ): Input: J i,k, and a time interval [t 1,t 2 ). Output: Total cumulative processor demands from higher-priority transactions τ j (1 j i 1) during [t 1,t 2 ). 1 l i k; // Record latest scheduled job of τ i. 2 d i,k t 2 ; 3 LSD i t 2 ; 4 if (i = 1) 5 then // No preemptions from higher-priority tasks. 6 return 0; 7 elsif (LSD i 1 LSD i ) 8 then // Get preemptions from τ j ( j,1 j<i)

23 9 // because τ j s schedule is complete before t return GetHPPreempt(i,k,t 1, LSD i ); 11 endif 12 // build S up to or exceeding t 2 for τ j (1 j<i). 13 for j = 1 to i 1 do 14 while (d j,lj < LSD i ) do 15 d j,lj +1 r j,lj + V j ; 16 r j,lj +1 ScheduleRT(j, l j + 1,C j,d j,lj +1); 17 l j l j + 1; 18 LSD j d j,lj ; 19 end 20 end 21 return GetHPPreempt(i,k,t 1, LSD i ); Function ScheduleRT(i, k, C i,d i,k ) (Algorithm 6.2) calculates the release time r i,k with known computation time C i and deadline d i,k. It starts with release time r i,k = d i,k C i, then iteratively calculates i (r i,k,d i,k ), the total cumulative processor demands made by all higher-priority jobs of J i,k during the interval [r i,k,d i,k ), and adjusts r i,k by accounting for the interferences from higher-priority transactions (Lines 5 to 12). The computation of r i,k continues until the interferences from higherpriority transactions do not change in an iteration. In particular, Line 9 detects any infeasible schedule. A schedule becomes infeasible under DS-FP if r i,k <d i,k 1 (k 0), i.e., release time of J i,k becomes earlier than the deadline of its preceding job J i,k 1. Function GetHPPreempt(i, k, t 1,t 2 ) scans the interval [t 1,t 2 ), adds up total preemptions from τ j ( j, 1 j i 1), and returns i (t 1,t 2 ), the cumulative processor demands of τ j during [t 1,t 2 ) from schedule S that has been built from CalcHP- Prempt. Function CalcHPPreempt(i, k, t 1,t 2 ) (Algorithm 6.3) calculates i (t 1,t 2 ),the total cumulative processor demands made by all higher-priority jobs of J i,k during the interval [t 1,t 2 ).Line7 ensures that ( j,1 j<i), τ j s schedule is completely built before time t 2. This is because τ i s schedule cannot be completely built before t 2 unless the schedules of its higher-priority transactions are complete before t 2.In this case, the function simply returns an amount of higher-priority preemptions for τ i during [t 1,t 2 ) by invoking GetHPPreempt(i,k,t 1,t 2 ), which returns i (t 1,t 2 ). If any higher-priority transaction τ j (j i) does not have a complete schedule during [t 1, t 2 ), its schedule S up to or exceeding t 2 is built on the fly (Lines 14 to 19). This enables the computation of i (t 1,t 2 ). The latest scheduled deadline of τ i s job, LSD i, indicates the latest deadline of τ i s jobs that have been computed. References Burns A, Davis R (1996) Choosing task periods to minimise system utilisation in time triggered systems. Inf Process Lett 58: Chen D, Mok AK (2004) Scheduling similarity-constrained real-time tasks. In: ESA/VLSI, pp

24 Chetto H, Chetto M (1989) Some results of the earliest deadline scheduling algorithm. IEEE Trans Softw Eng 15(10): Gerber R, Hong S, Saksena M (1994) Guaranteeing end-to-end timing constraints by calibrating intermediate processes. In: IEEE real-time systems symposium, December 1994 Gustafsson T, Hansson J (2004a) Data management in real-time systems: a case of on-demand updates in vehicle control systems. In: IEEE real-time and embedded technology and applications symposium, pp Gustafsson T, Hansson J (2004b) Dynamic on-demand updating of data in real-time database systems. In: ACM SAC Han CC, Lin KJ, Liu JW-S (1995) Scheduling jobs with temporal distance constraints. SIAM J Comput 24(5): Kang KD, Son S, Stankovic JA, Abdelzaher T (2002) A QoS-sensitive approach for timeliness and freshness guarantees in real-time databases. In: EuroMicro real-time systems conference, June 2002 Kuo T, Mok AK (1992) Real-time data semantics and similarity-based concurrency control. In: IEEE real-time systems symposium, December 1992 Kuo T, Mok AK (1993) SSP: a semantics-based protocol for real-time data access. In: IEEE real-time systems symposium, December 1993 Ho S, Kuo T, Mok AK (1997) Similarity-based load adjustment for real-time data-intensive applications. In: IEEE real-time systems symposium Lam KY, Xiong M, Liang B, Guo Y (2004) Statistical quality of service guarantee for temporal consistency of real-time data objects. In: IEEE real-time systems symposium Leung J, Whitehead J (1982) On the complexity of fixed-priority scheduling of periodic real-time tasks. Perform Eval 2: Liu CL, Layland J (1973) Scheduling algorithms for multiprogramming in a hard real-time environment. J ACM 20(1) Locke D (1997) Real-time databases: real-world requirements. In: Bestavros A, Lin K-J, Son SH (eds) Real-time database systems: issues and applications. Kluwer Academic, Dordrecht, pp Ramamritham K (1993) Real-time databases. Distrib Parallel Databases 1(1993): Ramamritham K (1996) Where do time constraints come from and where do they go? Int J Database Manag 7(2):4 10 Song X, Liu JWS (1995) Maintaining temporal consistency: pessimistic vs. optimistic concurrency control. IEEE Trans Knowl Data Eng 7(5): Xiong M, Ramamritham K (2004) Deriving deadlines and periods for real-time update transactions. IEEE Trans Comput 53(5): Xiong M, Ramamritham K, Stankovic JA, Towsley D, Sivasankaran RM (2002) Scheduling transactions with temporal constraints: exploiting data semantics. IEEE Trans Knowl Data Eng 14(5): Xiong M, Han S, Lam KY (2005) A deferrable scheduling algorithm for real-time transactions maintaining data freshness. In: IEEE real-time systems symposium Xiong M, Han S, Chen D (2006) Deferrable scheduling for temporal consistency: schedulability analysis and overhead reduction. In: IEEE international conference on embedded and real-time computing systems and applications, August 2006 Xiong M, Han S, Lam KY, Chen D (2008) Deferrable scheduling for maintaining real-time data freshness: algorithm, analysis and results. IEEE Trans Comput 57(7): Ming Xiong received his Ph.D. degree in Computer Science from University of Massachusetts Amherst in He is currently a member of technical staff at Bell Labs, Alcatel-Lucent. His research interests include database systems, real-time systems and mobile computing.

25 Song Han received his Bachelor of Science degree in Computer Science from Nanjing University, P.R. China in 2003 and Master of Philosophy degree in Computer Science from City University of Hong Kong in He is currently a Ph.D. student in the Department of Computer Sciences at the University of Texas at Austin. His research interests are real-time systems, database systems, wireless networks and data mining. He is a student member of the IEEE. Deji Chen received his Ph.D. degree in Computer Science from the University of Texas at Austin in He is currently a senior principal software engineer at Emerson Process Management. His research interests include real-time systems and wireless process control. Kam-Yiu Lam received the B.Sc. (Hons) degree on Computer Studies with distinction and Ph.D. degree from the City University of Hong Kong in 1990 and 1994, respectively. He is currently an Associate Professor in the Department of Computer Science, City University of Hong Kong. His current research interests are real-time database systems, real-time active database systems, mobile computing and distributed multimedia systems. Shan Feng received his Ph.D. degree in Computer Software and Theory from Chinese Academy of Science in He is currently an associate professor of Sichuan Normal University, Chengdu, China. His research interests include database systems, data mining theories, and real-time systems.