Threshold-Based Admission Control Policies for Multimedia Servers

Transcription

1 Threshod-Based Admission Contro Poicies for Mutimedia Servers ING-RAY CHEN AND CHI-MING CHEN Institute of Information Engineering, Nationa Cheng Kung University, Tainan, Taiwan, ROC Emai: Traditiona admission contro agorithms for on-demand mutimedia servers concern the acceptance decisions for new cients' requests so as to guarantee that continuous services to a cients are executed. These agorithms determine whether a new cient can be accepted, based on the consideration whether the underying hardware can satisfy the quaity of service QoS) requirements of admitted cient requests. In this paper, we consider a richer cass of admission contro agorithms that make acceptance/rejection decisions not ony to satisfy the hardware requirements of cient requests but aso to optimize the reward of the system based on a performance criterion as it services cients of different priority casses. We divide the server capacity into a number of `priority threshod vaues' based on which the system decides whether to accept cients of different priority casses dynamicay in order to maximize the system vaue. The resuting threshod-based admission contro agorithm is deveoped based on the idea that admission contro can be driven not ony by hardware requirements, but aso by knowedge regarding the workoad characteristics of cient requests, thus aowing the system to adjust dynamicay the threshod vaues in response to changes in cient workoad characteristics. We derive a cose-form expression for the vaue which the system can obtain when operating under the threshod-based agorithm as a function of mode parameters, and discuss how the server can utiize the anaytica soution at run time so as to maximize the system vaue dynamicay without vioating cients' continuity requirements. Received February 23, 996; revised February 6, 997. INTRODUCTION Mutimedia servers [, 2, 3, 4, 5] are designed to provide continuous services to cients on demand. This can be achieved by having the server periodicay execute the cients' tasks e.g. for media data processing) such that the periodic deadine requirement of each cient is satis"ed. A promising approach for guaranteeing continuous services is based on the design concept of capacity reservation [6] by which a fraction of the server capacity is reserved for each new cient, and once a reservation has been made, the cient is guaranteed of the avaiabiity of the server capacity reserved unti it terminates. For exampe, in designing an on-demand mutimedia server [4], the capacity reservation concept is impemented by aocating a portion of the server capacity to retrieve a speci"ed number of disk bocks in a repeated service cyce for each admitted cient, so as to meet the pay-back rate requirements of a admitted cients. When the server capacity is used up by existing cients, a newy arriving cient may be rejected so as to guarantee continuous services to cients that have been admitted. The rejected cient is then `ost', representing some type of oss to the system in overoaded situations. One issue in the design of such on-demand mutimedia servers is to make the oss rate of cients as sma as possibe when the system is overoaded. This issue may invove dynamicay owering the quaity of service QoS) eves of existing cients so as to make room for newy arriving cients and may invove the design of some negotiation protocos [7]. Another design issue is an admission contro poicy based on which the server accepts/rejects new requests. This paper concerns the second design issue. Existing admission contro agorithms make acceptance/rejection decisions merey based on the consideration whether the underying hardware can satisfy the QoS requirements of cients [8, 4, 9, 0], e.g. based on the payback rate requirements of media streams. Two casses of admission contro agorithms have so far been considered in the iterature, namey, `deterministic' and `best-effort.' Rangan et a. [4, 9] deveoped deterministic admission contro agorithms by considering different ways of performing data pacement and disk access scheduing. They derived a formua for the maximum number of cients which the system can admit based on the theoretica worst-case time bounds with absoute guarantees. Vin et a. [0] subsequenty compared deterministic agorithms with predictive agorithms which aow momentary vioations of the cients' QoS requirements to be toerated, as ong as the fraction of media data deivered on time is arger than a speci"ed threshod vaue, say α, speci"ed as part of a cient's QoS requirement. Based on this concept, they deveoped predictive admission contro agorithms using average-case service times obtained from extrapoation data based on past measurements. They THE COMPUTER JOURNAL, Vo. 39, No. 9, 996

2 758 I.-R. CHEN AND C.-M. CHEN caimed by simuation that the maximum number of cients which can be admitted by the server with predictive services is greaty increased with the server utiization being greaty improved, when compared with deterministic services. It was aso demonstrated that these bene"ts are obtained without sacri"cing the QoS requirements speci"ed by cients requesting predictive services. Another study of best-effort admission contro is by Chang and Zakhor [8] who investigated a cass of statistica admission contro strategies for buffer management for variabe bit rate VBR) video servers. They used a statistica QoS contro strategy to determine whether a cient can be admitted based on a statistica estimation of the probabiity that the tota data requested by a of the users exceeds the server capacity. A new cient to the system is rejected if this probabiity at the arriva instant is found to be greater than a speci"ed threshod probabiity vaue. They showed that statistica admission contro is more effective than deterministic admission contro for interactive video server systems. A these past studies discussed above do not consider priority scheduing in operating environments in which mutipe service casses exist. Their main research goa was to accept as many cients as possibe without vioating or compromising too much of their QoS requirements. In this paper, we address priority scheduing issues and deveop admission contro agorithms which make acceptance/rejection decisions not ony to satisfy the QoS requirements of cient requests but aso to make the system bene"t the most from the perspective of `reward optimization'. We borrow the concept of transaction vaues in scheduing rea-time transactions [, 2] and introduce the notions of `reward' and `penaty' associated with each cient into our cost mode. Speci"cay, we consider that every cient can be assigned a reward indicating its vaue to the system e.g. monetary vaue) when the cient is successfuy serviced, and conversey a penaty indicating the negative vaue e.g. oss of pro"t) imparted to the system when the cient is rejected in overoaded situations. These positive/negative parameters re#ect the bene"t/oss to the server system. Notice that ony specifying the reward parameter without specifying the penaty parameter, or vice versa, is not suf"cient. For exampe, ignoring penaties wi ead to the naive design of reserving most or a of the system resources for ow-priority cients in situations where ow-priority cients arrive more frequenty than highpriority cients, as there is no consequence in rejecting a high-priority cient which may otherwise impose a very high penaty. The motivation for introducing the reward/penaty parameters is to create a performance index which accounts for both the QoS and priority importance) requirements of the cient. It provides a basis for mathematicay assessing the Scheduing rea-time transactions with vaues aso concerns maximizing the system's added vaue; however, the main thrust is to design a transaction processing protoco by which the execution sequence of transaction operations can be ordered, possiby by aborting existing transactions or by deaying the commitment of transactions, so as to maximize the system vaue. trade-off between priority reservation and no priority reservation designs. Under the priority reservation scheme, the server can reserve its capacity discriminativey for different priority-cass cients for the purpose of `reward optimization', considering that a high-priority user is associated with a higher `vaue' if it is served successfuy and, correspondingy, a higher `penaty' if it is rejected. With this reward/penaty concept, the design of admission contro agorithms can be considered as a reward optimization probem, i.e. designing an admission contro agorithm which can dynamicay adjust priority reservation poicies as the input characteristics of cient requests change dynamicay, so as to maximize the system vaue. Dynamic workoad change can happen during the peak/off-peak hours of an on-demand mutimedia server system. In this paper, we deveop a cass of `threshod-based' admission contro agorithms, with `threshod' referring to the amount of server capacity reserved for different priority cients. We divide the server capacity into a number of `priority threshod vaues' based on which the system can decide whether to accept high-priority or owpriority cients dynamicay in order to maximize the system vaue. The resuting threshod-based admission contro agorithm is deveoped based on the idea that admission contro can be driven not ony by hardware requirements, but aso by knowedge of the workoad characteristics of cient requests, thus aowing the system dynamicay to adjust the threshod vaues in response to changes in cient workoad characteristics. We derive a cose-form expression for the vaue which the system can obtain when operating under the threshod-based agorithm as a function of mode parameters, and discuss how the server can utiize the anaytica soution at run time so as to maximize the system vaue dynamicay. The contribution of our work with respect to previous works is that we vitaize the roe of an admission contro agorithm from a passive roe, i.e. preventing system overoad, to an active roe, or maximizing system performance whie sti satisfying requests' continuity requirement. We achieve this goa by identifying the best priority reservation strategy when given a set of cient workoad characteristics. Our approach can hande mutipe priority casses. The rest of the paper is organized as foows. Section 2 presents the system mode based on which severa admission contro agorithms are anaysed, namey, free-threshod, "xed-threshod and dynamic-threshod admission poicies. A performance criterion is de"ned which uses a combined reward/penaty performance metric for evauating various threshod-based agorithms. Using simpe queueing theory arguments, Section 3 derives cosed-form expressions based on a performance metric in the form of PO x t, s) where t is a set of priority threshod vaues and s is a set of input parameter vaues characterizing the behaviour of arriving cients in different priority casses. Section 4 discusses the optimaity of the dynamic threshod-based agorithm, that is, being abe to "nd an optima t which maximizes PO x t, s) for each s given. It aso discusses how the anaytica expressions derived in Section 3 can be used by the server THE COMPUTER JOURNAL, Vo. 39, No. 9, 996

3 THRESHOLD-BASED ADMISSION CONTROL POLICIES 759 system at run time to adjust dynamicay its threshod vaues so as to maximize the system vaue. Section 5 shows some numerica exampes and gives physica interpretations of the resut. Finay, Section 6 summarizes the paper and outines some future research areas. 2. SYSTEM MODEL We assume that the on-demand mutimedia server adopts the capacity reservation mechanism such that a server capacity reservation is made at the time a new cient arrives. A new cient is accepted if the remaining capacity can accommodate it, otherwise, the cient is turned away. Consequenty, there exists a maximum number of cient requests that the system can service without overoading, as has been addressed in previous works in admission contro [8, 0]. Note that the above argument hods for both deterministic and best-effort admission contro. For ease of exposition, we "rst consider the case when there exist two priority casses of cients, each cass being characterized by its own arriva/departure rates as we as its reward/penaty vaues. We wi ater reax this assumption in Section 3. For trackabiity 2, we assume that the inter-arriva times of high-priority and ow-priority cients are exponentiay distributed with average times of /λ h and /λ, respectivey. Once a reservation is made, a cient is assured of the server capacity unti its task is competed. The rea-time computationa requirement of each cient is characterized by a period T and a computation time C within the period. To provide a rea-time, continuous service to each cient, a thread may be created by the server at the time the cient is admitted into the system and is invoked afterward periodicay, utiizing a fraction C/ T of the server capacity, unti the cient competes its requested service. For simpicity, the inter-departure time of either the high-priority or owpriority cients is assumed to be exponentiay distributed with an average time of /, athough the anaysis which foows can hande different departure rates. The capacity reservation mechanism of the server system is modeed as foows. We assume that a high-priority cient reserves a fraction /n of the capacity corresponding to C/ T above), whereas a ow-priority cient reserves a fraction /m, m n, of the capacity. In genera, m n since a ow-priority cient may request a ower QoS requirement than a high-priority cient. This paper considers the specia case in which m n, corresponding to the case where a cients' hardware requirement e.g. payback rate of media streams) is the same but some cients are more important than others. From the perspective of the server system, the system behaves as if it contains n capacity sots. When a sots are used up, the server rejects a newy arriving cient so as to guarantee continuous services to a 2 Our approach can be appied to genera distributions e.g. a semi- Markov mode) except that we wi not be abe to obtain anaytica soutions and aso a software too which anayses stochastic modes such as SHARPE [5] wi have to be used to obtain numerica soutions on a case by case basis. cients that have been admitted. An exampe for which this assertion is justi"ed occurs in the design of a rea-time on-demand mutimedia server [4] where the parameter n corresponds to the maximum number of subscriber requests with the same payback rate that can be serviced by the server. In such cases, as ong as the system does not admit over n cient requests, continuous services to a admitted cient requests can be guaranteed. The pay-off to the server when a cient competes its service is characterized by each cient's reward and penaty parameters. We assume that the rewards of high-priority and ow-priority cients are v h and v, respectivey, with v h v, and the penaties to the system when high-priority and owpriority cients are rejected are q h and q, respectivey, with q h q. The performance metric being considered in the paper takes both rewards and penaties of cients into consideration. It is caed the system's tota pay-off rate, de"ned as the average amount of reward received by the server per time unit. In other words, under a particuar admission poicy if the system on average services N h high-priority cients and N ow-priority cients per unit time whie rejects M h highpriority cients and M ow-priority cients per unit time, then the system tota pay-off rate is N h v h + N v M h q h M q. Formay, the probem we are thus interested in soving is to identify the best admission contro poicy under which this performance metric is maximized, as a function of mode input variabes, incuding n, λ h, λ,, v h, v, q h and q de"ned above. Tabe summarizes the notation used in this paper. 3. THRESHOLD-BASED ADMISSION CONTROL In this section, we deveop three threshod-based admission contro agorithms in increasing order of reward maximization, at the expense of increased time compexity, and anayse their behaviours. We "rst derive anaytica expressions for the system reward obtainabe when ony two priority casses exist. Later we wi extend the anaysis to the more genera case when more than two priority casses exist. 3.. Free threshod The simpist admission poicy, termed `free-threshod', is to accept any new arriving cient regardess of its priority type, as ong as there is a sot to accommodate it. In essence, it is equivaent to the "rst come, "rst served poicy without appying any reward-based contro. We wi use this poicy as the base poicy against which other more sophisticated admission poicies can be compared. Essentiay, under this poicy, there is no priority distinction among cients and the system behaves ike a cassic M/M/n/n system [4] with the arriva rate λ λ h + λ and the departure rate i when there are i cients in the system. The oss rate of cients in THE COMPUTER JOURNAL, Vo. 39, No. 9, 996

4 760 I.-R. CHEN AND C.-M. CHEN TABLE. Notation. λ h Arriva rate of high-priority cients λ Arriva rate of ow-priority cients Departure rate of cients v h Reward of a high-priority cient if the cient is serviced successfuy v Reward of a ow-priority cient if the cient is serviced successfuy q h Penaty of a high-priority cient if the cient is rejected on admission q Penaty of a ow-priority cient if the cient is rejected on admission POx Tota system pay-off rate under admission poicy x, e.g. income rate of the company running the on-demand mutimedia service business n Maximum number of server capacity sots for servicing cients n h Number of sots reserved for high-priority cients ony, 0 n h n n Number of sots reserved for ow-priority cients ony, 0 n n and aso n h + n n n m Number of sots that can be used to service either type of cient, n m n n h n T A time period in which a cient's computation is executed periodicay C The amount of computation time within T for each cient; C/T /n this case is equa to ) λh + λ n n! λ h + λ ) n ) λh + λ j, + j where the "rst term is the coective arriva rate of high- and ow-priority cients and the second term is the probabiity of a n sots being occupied. Using ony one component in the state representation, the M/M/n/n mode does not keep track of the number of highpriority or ow-priority cients in each state. However, since with probabiity λ h /λ h + λ ) a new cient is a high-priority cient and conversey with probabiity λ /λ h + λ ) it is a ow-priority cient, each state i representing that there are i cients in the system in the steady state) can be associated with a pay-off reward rate of i v h λ h + v λ h + λ λ λ h + λ ). On the other hand, state n representing that a sots are used up) can be associated with a penaty rate of q h λ h + q λ. Consequenty, the system pay-off rate under the freethreshod poicy, PO free, can be obtained by summing the pay-off reward rates weighted by their individua state probabiities, and subtracting the penaty rates due to rejection when a n sots are occupied, i.e. PO free n,λ h,λ,,v h,v,q h,q ) n i v h λ h +v λ ) λ h +λ λ h +λ ) λh +λ i i! n ) λh +λ j + i j ) λh +λ n n! q h λ h +q λ ) n ) λh +λ j +. j ) Note that here the tota system pay-off rate PO free is expressed as a function of n, λ h, λ,, v h, v, q h and q Fixed threshod Under the "xed-threshod admission poicies, we aocate n h sots, n h n, to high-priority cients ony, whie the remaining sots n n n h sots are aocated to owpriority cients ony. When a the sots aocated to highpriority correspondingy ow-priority) cients are exhausted, a new arriving high-priority ow-priority) cient is rejected by the server even if there are sti avaiabe sots in the sots aocated to ow-priority high-priority) cients. This situation is ikey when we have a priori knowedge of the arriva rates of cients such that it is justi"ed to reserve some capacity for high- or ow- priority cients in order to maximize the system pay-off. In this case, the server behaves as if it is managing two separate, concurrent queues: one is an M/M/n h /n h queue for high-priority cients ony with the arriva rate equa to λ h, service rate equa to i when there are i high-priority THE COMPUTER JOURNAL, Vo. 39, No. 9, 996

5 THRESHOLD-BASED ADMISSION CONTROL POLICIES 76 cients being serviced, and the number of sots equa to n h, whie the other is an M/M/n /n queue designated for owpriority cients ony with the arriva rate equa to λ, service rate equa to i when there are i ow-priority cients being serviced, and the number of sots equa to n. The oss rate of cients in this case is equa to the sum of that due to ow-priority cients and that due to high-priority cients, i.e. n h! λ h + j ) nh λh n! ) j + λ n + λh j ) n λ λ ) j. By associating a pay-off reward rate of i v h correspondingy i v ) for state i in the M/M/n h /n h queue for high-priority correspondingy in the M/M/n /n queue for ow-priority) cients and subtracting the penaty rate for the case when n h correspondingy n ) sots are used up for high-priority ow-priority) cients, we can compute the system pay-off rate as PO fixed n h,n,λ h,λ,,v h,v,q h,q ) + i n i i! i v h + j ) i λh j ) j λh ) i λ i! i v n + n h! λ h q h + j ) nh λh ) j λh ) j λ 2) aways "s in the sots in n h and n for high- and ow-priority cients, respectivey, before "ing in a sot in n m. This poicy encompasses the previous two admission poicies: in the case when n m 0, this poicy degenerates to the "xed-threshod admission poicy, whie in the case when n h n 0, it degenerates to the free-threshod poicy. It aso covers the interesting case of n 0 wherein highpriority cients can use the n m sots open to both high- and ow-priority cients as ong as there is a space), but no owpriority cients can use any of the n h sots aocated to highpriority cients. The cosed-form soution to the system pay-off rate under the dynamic admission poicy can be obtained by considering a two-eve hierarchica mode. The high-eve mode is ike the one for the free-threshod admission poicy, i.e. an M/M/n m /n m queue with the arriva rate equa to h +, and the service rate equa to. Here, h and denote the arriva rates of high-priority and ow-priority cients after n h and n sots have been occupied by highpriority and ow-priority cients, respectivey. These two arriva rates associated with the `spi-over' processes which are Markov processes themseves [3]) can be obtained from two ow-eve modes, one for each type of cients, ike the ones we have used for the "xed-threshod admission poicy. Speci"cay, and n h! h λ h + j n! λ n + j ) nh λh ) j λh ) n λ λ ) j. The system pay-off rate in this case is the sum of that due to the n h and n sots assigned to high- and ow-priority cients ony, and that due to the sharabe n m sots, i.e. n! λ q n Dynamic threshod j ) n λ λ ) j. Under the dynamic-threshod admission poicy, the n sots are divided into three parts: n h, n and n m, with n h speci"cay aocated to high-priority cients, n aocated to ow-priority cients whie the remaining n m sots shareabe with both types of cients. When a high-priority correspondingy a ow-priority) cient arrives, if there is a sot avaiabe in the n h correspondingy n )orn m part, then the cient is accepted; otherwise, it is rejected. The poicy PO dynamic n h,n m,n,λ h,λ,,v h,v,q h,q ) + i n i i! i v h + j ) i λh j ) j λh ) i λ i! i v n + ) j λ + PO free n m, h,,,v h,v,q h,q ), 3) THE COMPUTER JOURNAL, Vo. 39, No. 9, 996

6 762 I.-R. CHEN AND C.-M. CHEN where the expression for PO free...) is given earier in Equation. We check the boundary conditions beow. For the specia case when n h n 0, we have h λ h, λ, the "rst two terms being zeros, and therefore PO dynamic 0,n,0,...) PO free n,...) in which the dynamic admission poicy degenerates to the free admission poicy. For the specia case when n m 0, we have PO free 0,...) q h h q, and therefore PO dynamic n h,0,n,...)po fixed n h,n,...)in which the dynamic admission poicy degenerates to the "xed admission poicy. Equation 3 correcty satis"es these boundary conditions. PO M fixed n...n M,λ...λ M,,v...v M, q...q M ) M n k i! i v k n k i + k M λ n k! kq k n k + k j j ) nk λk ) i λk ) j λk ) j λk. 5) 3.4. Mutipe priority casses Equations, 2 and 3 can easiy be generaized to the case when there exist more than two priority casses. Assume that there are M priority casses, of which cass is the highest priority cass, whie cass M is the owest. Cass k, k M, is characterized by its own set of parameters λ k, v k, q k ). Other than the free agorithm, the threshod vaue speci"cay reserved for cass k is n k, with M k n k n for the "xed agorithm and n m + M k n k n for the dynamic agorithm with n m being the threshod vaue shareabe to a priority casses. The generaization is straightforward and here we wi ony show the resuts without proof. Equations 4, 5 and 6 beow give these reward rate expressions under the free, "xed and dynamica contro agorithms, respectivey, when M priority casses exist. PO M free n,λ...λ M,,v...v M, q...q M ) n M i i M q k λ k k where λ M k λ k. k v k λ k λ λ n! n + j ) λ i i! n λ + ) n j ) λ j ) j 4) PO M dynamic n...n M, n m,λ...λ M,,v...v M, q...q M ) M n k i! i v k n k i + k j ) i λk ) j λk + PO M free n m,... M,,v...v M, q...q M ) 6) where the expression for k was derived earier in Section ALGORITHM COMPLEXITY AND SOLUTION TECHNIQUE The inputs to the threshod-based admission contro agorithms discussed above are the arriva and departure rates, i.e. λ h, λ and, pus the reward and penaty parameters, i.e. v h, v, q h and q. The output is the overa system vaue, PO free for free, PO fixed for "xed and PO dynamic for dynamic. In particuar, for the ast two outputs, we are interested in obtaining the system vaue obtainabe at optima conditions, that is, the argest PO fixed optima vaue n h, n ) under the "xed agorithm, and the argest PO dynamic optima vaue n h, n m, n ) under the dynamic agorithm. Determining the optima point in these cases can be done by enumerating a possibe combinations and appying Equation 2 or Equation 3 to seect the highest vaue. Speci"cay, the number of possibe cases, which is the same as the number of ways of dividing n into K distinct groups threshods), is Cn + K, K ) with Cx, y) x!/y!x y)!). Consequenty, for the "xed and dynamic agorithms discussed in Subsections 3.2 and 3.3, the number of cases to be tested wi be Cn +, ) n + and Cn + 2, 2) n + 2)n + )/2, respectivey. The time compexity invoved in enumerating and appying Equation 2 or 3 is thus On) for "xed and is On 2 ) for dynamic. It is easy to show that under a given set of parameter vaues, there aways exists an optima threshod vaue set THE COMPUTER JOURNAL, Vo. 39, No. 9, 996

7 THRESHOLD-BASED ADMISSION CONTROL POLICIES 763 FIGURE. A 3-D graph showing n h, n m, n ) vs. PO dynamic. The maximum point is 7, 3, 0). of n h, n m, n ) under which the system vaue is maximized under the dynamic agorithm. The reason is twofod. First, the number of cases which can be enumerated for a given n under the dynamic agorithm is "nite, i.e. n + 2)n + )/2 to be exact. Therefore, by using Equation 3 to compute the system vaue obtained for each case, we can determine the optima set which yieds the maximum system vaue. Second, a the cases enumerated by either the free or "xed agorithm are just subcases which can be enumerated under the dynamic agorithm. The free agorithm generates one specia case for which n h n 0 and n m n, whie the "xed agorithm generates n + specia cases for which n m 0. Therefore, the optima threshod vaue set wi aways be uncovered by the dynamic agorithm. There are two ways of appying the anaysis resut obtained in this paper to rea-time admission contro. The "rst way is to staticay generate a tabe and then do a tabe ookup at run time. This method is appicabe when v h, v, q h and q can staticay be determined by the system designer at the design time based on the characteristics of cient service casses and the appication environment. In this case, we can evauate optima n h, n m, n ) sets staticay for various combinations of λ h, λ and which are ikey to change dynamicay. A symboic mathematica software package such as Mathematica [6] can be used for this purpose. Figure shows a three-dimensiona graph generated by Mathematica. It shows PO dynamic as a function of n h, n m, n ) for the case when n 20,v h 0,v 2,q h 2,q and λ h 5,λ 40 and. Note that n m is not shown on the graph because it is equa to n n h n. The optima set as determined by Mathematica in this case is 7, 3, 0). After the tabe is staticay estabished this way to cover a range of cient arriva and departure rates, the system can a) coect run-time cient arriva and departure data periodicay; b) estimate the average arriva and departure rates in the period; and c) adjust the optima threshod vaue set by using a ook-up tabe so as to optimize the system pay-off vaue dynamicay on a period by period basis. This method is feasibe for video server designs since it is reasonabe to assign cients in different priority casses with distinct reward/penaty vaues at the design time based on the beief of the designer. The second way is to treat v h, v, q h and q aso as variabes and appy enumeration methods and Equation 3 at run-time to seect the optima threshod vaues. Since the agorithm's compexity is On 2 ), it shoud be done ony periodicay, perhaps by executing a background process which periodicay estimates average parameter vaues and THE COMPUTER JOURNAL, Vo. 39, No. 9, 996

8 764 I.-R. CHEN AND C.-M. CHEN recomputes the next set of optima n h, n m, n ) vaues to be used by the server in the next period. The server can continue using the od set of n h, n m, n ) vaues to admit users whie the background process computes the new optima set. 5. NUMERICAL EXAMPLES We use the design of an on-demand mutimedia server [0] as an exampe to demonstrate the utiity of our anaysis resut. One reported experiment used an array of 28 disks each with a storage capacity of 0.5 Gbyte to impement the server. The payback rate is assumed to be 30 frames/s per cient request. Successive media bocks each of 52 kbyte) of a video stream are assumed to be randomy stored on disk. Under the hardware constraints of the disk array used the maximum number of cient requests that can be served concurrenty was found to be around n 6 if deterministic admission contro is considered and n 84 if best-effort admission contro is considered with a read-ahead buffer of media bock per cient. The atter is different from the former in that the server admits cients based on the observed performance characteristics of the server with predictive guarantee, rather than based on theoretica worstcase time bounds with absoute guarantee [0]. It shoud be noted that this anaysis was purey based on resource capacity imitations, without considering the importance or criticaity of requests. Tabes 2 and 3 ist the optima n h, n m, n ) threshod vaue sets with respect to some seected sets of mode parameter vaues characterizing various cient workoad possibiities for the server system, for n 6 and n 84, respectivey. Tabes 2 and 3 are generated by appying Equations and 3. In addition, the vaues isted in the coumn abeed `optima n h, n m, n )' are uncovered by the dynamic admission contro agorithm based on the mechanism discussed in Section 4. Here we observe that the pay-off rate at the optimizing condition under dynamic-threshod admission can be much higher than that under free-threshod admission. Moreover, the tota pay-off rate can be negative if requests are served indiscriminativey. Another observation is that as the arriva rate λ h ), reward v h ) or penaty q h ) of high-priority cients increases, more sots wi be reserved for high-priority cients. An exampe is entry of Tabe 2 for which the number of sots reserved for high-priority cients is zero and therefore a high-priority cient who sti presumaby pays more) wi have to compete with ow-priority cients for the shareabe sots. The reason is that the arriva rate of highpriority cients in entry is an order of magnitude ower than that of ow-priority cients i.e. versus 0) and aso the reward of accepting a high-priority cient is not high compared to that of accepting a ow-priority cient i.e. 2 versus ). The ast entry of Tabe 2 shows that as both the arriva rate and reward of high-priority cients increase reative to those of ow-priority cients), more and more sots wi be reserved for high-priority cients by the system in order to maximize the tota system pay-off. Figure 2 demonstrates the effect of appying dynamic TABLE 2. Optimizing threshod vaues n 6). λ h,λ,,v h,v,q h,q ) optima dynamic free n h, n m, n ) PO PO, 0,, 2,, 2, ) 0,7,9) 2, 0,, 5,, 2, ),7,8) 5 4, 0,, 0,, 2, ),7,8) 9 8 5, 0,, 2,, 2, ) 3,0,3) 5 4 5, 0,, 5,, 2, ) 5,0,) , 0,, 0,, 2, ) 6,0,0) , 0,, 2,, 2, ) 8,8,0) 4 2 0, 0,, 5,, 2, ) 2,4,0) , 0,, 0,, 2, ) 4,2,0) TABLE 3. Optimizing threshod vaues n 84). λ h,λ,,v h,v,q h,q ) optima dynamic free n h, n m, n ) PO PO 0, 00,, 2,, 2, ) 7,60,7) , 00,, 5,, 2, ) 0,68,6) , 00,, 0,, 2, ) 2,72,0) , 00,, 2,, 2, ) 50,34,0) , 00,, 5,, 2, ) 56,28,0) , 00,, 0,, 2, ) 60,24,0) , 00,, 2,, 2, ) 84,0,0) , 00,, 5,, 2, ) 84,0,0) , 00,, 0,, 2, ) 84,0,0) threshod admission contro more ceary. It dispays the difference between the optima pay-off rate and that without contro i.e. with free-threshod), with λ h varying in the range of [0, 50] in increments of 0 and λ varying in the range of [50, 50] in increments of 50, and with n 00. We set the reference reward/penaty parameter vaues for ow-priority cients at and et v h /v > q h /q, meaning that the oss the system suffers from rejecting a high-priority cient is ower in absoute vaue than the reward that it receives from accepting the same high-priority cient. We study this case because it is generay true that the system woud not ose a vaue due to turning away a cient more than it woud gain due to accepting the same cient, especiay for high-priority cients. The trend exhibited in Figure 2 can be expained as foows. When the system oad is ight corresponding to the eft part of the graph) the effect of threshod-based admission contro is not signi"cant because the system can accommodate a new arriving cient with a high probabiity, so that free admission is just as good as threshod-based admission. As the system oad becomes moderate to heavy corresponding to the midde part of the graph) the effect of threshod admission contro becomes manifested because the server can effectivey manage the server capacity with threshods) based on the knowedge regarding workoad characteristics so as to optimize the payoff rate. Finay, when the oad is very heavy corresponding to the right part of the graph) the effect of threshod admission contro becomes ess signi"cant again because too many cients are ost even if the dynamic contro agorithm THE COMPUTER JOURNAL, Vo. 39, No. 9, 996

9 THRESHOLD-BASED ADMISSION CONTROL POLICIES 765 PO dynamic PO free λ 50 λ 00 λ 50 n 00 v h 0 v q h 2 q FIGURE 2. Difference in reward rate as a resut of appying threshod-based reward-optimization admission contro. λ h is in effect. It shoud be noted that the trend exhibited in Figure 2 is not universay true for a cases. It depends on the reative ratios of v h /v and q h /q and, in genera, the characteristics of the workoad for the server system in question. The equations derived in the paper aow the designer to identify the optimizing n h, n m, n ) set under a speci"ed workoad condition, and quantitativey predict how much bene"t the system can gain e.g. in terms of reward rate) by empoying the threshod-based admission contro agorithm. 6. CONCLUSIONS In this paper, we have anaysed a design concept for impementing reward-optimization admission contro agorithms for on-demand mutimedia systems. The design concept is based on the idea that an admission contro program shoud consider not ony the underying hardware imitation of the system, but aso the bene"t it can bring to the system as a resut of accepting/rejecting cient requests. We iustrated our concept by using the system's reward rate e.g. the income rate of a company that runs the ondemand mutimedia server business) as a metric to guide the design of admission contro agorithms. We investigated a cass of threshod-based admission contro agorithms for maximizing this metric. Anaytica expressions for the system pay-off rate under these threshod-based admission contro agorithms were derived. They can be used to determine the optima condition for accepting/rejecting cient requests and hep the system designer determine in a quantitative way how much bene"t the system wi gain as a resut of appying a threshod-based admission contro agorithm. Finay, the effectiveness of our approach was demonstrated by a reaistic on-demand mutimedia server. Our approach is particuary usefu for situations where the system's cient-priority/workoad characteristics may change dynamicay during its peak/off-peak hours. The technique presented in the paper can be used to adjust dynamicay the threshod vaues based on the system characteristics so that the system can aways receive the best reward without vioating its continuity requirement. Some future research areas incude a) couping the concept of reward-optimization with owering the quaity of service QoS) eves of existing cients so as to make room for new arriving cients; and b) designing threshod-based admission contro agorithms for on-demand mutimedia systems in which cients may have different rewards or penaties when successfuy or unsuccessfuy served as we as different QoS requirements. ACKNOWLEDGEMENTS This work was supported in part by the Nationa Science Counci of R.O.C. under grant NSC E REFERENCES [] Mei, G. G., Lin, M. H., Hu, L. and Chang, H. 992) A reatime mutimedia system for video appications. 26th IEEE Conf. Signas, Systems and Computers, Paci"c Grove, CA, pp [2] Oomoto, E. and Tanaka, K. 993) OVID: Design and impementation of a video-object database system. IEEE Trans. Know. Data Engng, 5, [3] Oyang, Y. J., Wen, C. H., Cheng, C. Y., Lee, M. H. and Li, J. T. 995) A mutimedia storage system for on-demand payback. IEEE Trans. Consumer Eectronics, 4, [4] Rangan, P. V., Vin, H. M. and Ramanathan, S. 992) Designing an on-demand mutimedia service. IEEE Commun., 30, [5] Vina, A., Lerida, J. L., Moano, A., and de Va, D. 994) Rea-time mutimedia systems. 3th IEEE Symp. Mass THE COMPUTER JOURNAL, Vo. 39, No. 9, 996

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