Delay Analysis of Maximum Weight Scheduling in Wireless Ad Hoc Networks
|
|
- Andra Peters
- 6 years ago
- Views:
Transcription
1 1 Deay Anaysis o Maximum Weight Scheduing in Wireess Ad Hoc Networks ong Bao e, Krishna Jagannathan, and Eytan Modiano Abstract This paper studies deay properties o the weknown maximum weight scheduing agorithm in wireess ad hoc networks. We consider wireess networks with either onehop or muti-hop ows. Speciicay, this paper shows that the maximum weight scheduing agorithm achieves order optima deay or wireess ad hoc networks with singe-hop traic ows i the number o activated inks in one typica schedue has the same order with the number o inks in the network. This condition woud be satisied or most practica wireess networks. This resut hods or both i.i.d and Markov moduated arriva processes with two states. For the muti-hop ow case, we aso derive tight backog bounds in the order sense. I. INTRODUCTION Wireess scheduing has been known to be a key probem or throughput/capacity optimization in wireess networks. The we-known maximum weight scheduing agorithm has been proposed by Tassiuas in his semina paper 1] where he proved its throughput optimaity. atter deveopments in this area incude extension o this maximum weight scheduing agorithm to wireess networks with rate/power contro ], 3], network contro when oered traic is outside the capacity region 4], and other scheduing poicies with owercompexity 5]-8]. Whie most existing works in the area o stochastic network contro ocused on throughput perormance o optima and suboptima scheduing poicies, deay properties o most scheduing poicies proposed or wireess ad hoc networks remain unknown. In this paper, we study backog/deay properties o the maximum weight scheduing agorithm in wireess ad hoc networks. There are some recent works which investigated backog/deay bounds or the supoptima maxima scheduing agorithm in wireess ad hoc networks and maximum weight scheduing agorithm in the downink/upink o ceuar networks. Speciicay, in 13] Neey showed that maxima scheduing achieves deay scaing o O (1/(1 ρ)) or traic inside the reduced stabiity region derived in 8]. This reduced stabiity region can be as sma as 1/I o the capacity region, where I is the maximum number o inks in any ink intererence set which do not interere with one another. In 14], 15], Neey aso proved the order optima deay or the maximum weight scheduing agorithm in the wireess ceuar upink/downink with ON/OFF wireess inks. Note that the capacity region in the ceuar setting can be expicity described which signiicanty eases the backog/deay anaysis. Average backog bounds were derived or maximum weight This work was supported by NSERC Postdoctora Feowship and by ARO Muri grant number W911NF The authors are with Communications and Networking Research Group, Massachusetts Institute o Technoogy, Cambridge, MA, USA. Emais: ongbe, krishnaj, modiano}@mit.edu. scheduing in severa works ], 4], 10], 9]. These backog bounds were obtained by bounding the maximum transmission rates and the number o arrivas in each time sot which are, thereore, not tight in genera. There are some other works which investigate exponents or the tais o queue backogs in the wireess ceuar setting 11], 1]. In this paper, we consider a wireess ad hoc network with either one-hop and muti-hop traic ows. We show that average deay or the case o one-hop traic ows scaes as O (1/(1 ρ)) i we can construct a set o distinct schedues to cover the network where the number o activated inks in each o these schedues has the same order with the number o network inks. This condition woud be satisied or most practica arge-scae wireess networks. This deay scaing hods or both i.i.d and Markov moduated traic arriva processes with at most two states. These resuts are stated in Propositions 4 and 5 o the paper. To the best o our knowedge, these are the irst deay optima resuts or the maximum weight scheduing agorithm in wireess ad hoc networks. For wireess ad hoc networks with mutihop traic ows, we aso derive a tight backog bound which scaes as O (N/(1 ρ)) where N is the number o wireess nodes. The remaining o this paper is organized as oows. Deay anaysis or singe-hop traic ows is presented in section II. In section III, we derive backog bounds or wireess networks with mutihop traic ows. II. ANAYSIS OF SINGE-HOP FOW CASE A. System Modes and Assumptions We mode a wireess ad hoc network as directed graph G = (V, E) where V is the set o wireess nodes and E is the set o wireess inks. Suppose the cardinaities o V and E are N and, respectivey. We consider singe-hop traic ows in this section. Data rom a ows traversing a particuar ink is buered at the corresponding transmitter o the ink. Assume time is sotted with ixed-size sot intervas. For now, traic arriving to source nodes o singe-hop ows is assumed to be independent and identicay distributed (i.i.d) over time. Assume that packets arriving during time sot t can ony be transmitted rom time sot t + 1 at the eariest. et denote by A (t) the number o packets arriving at ink in time sot t and µ (t) the number o packet transmitted on ink in time sot t. For simpicity, assume that µ (t) = 1 i ink is schedued in time sot t, otherwise µ (t) = 0. In the remaining o this paper, we wi use r to describe a coumn vector with eements r denoting quantities such as queue ength, schedued inks, etc. The queue evoution or the ow at ink can be written
2 as oows: (t + 1) = (t) µ (t) + A (t). (1) Assume that ony backogged inks are schedued, it can be veriied that this queue evoution equation hods or arbitrary (t) and µ (t). Regarding the scheduing, we consider the we-known maximum weight scheduing agorithm which is known to achieve the capacity region 1]. The maximum weight scheduing agorithm determines the optima schedue µ (t) based on the ink queue backogs as oows: µ (t) = argmax µ(t) S (t)µ (t) () where S denotes the set o a possibe easibe schedues according some intererence constraints. In this section, we are going to derive the deay bound or this scheduing poicy assuming that arriva traic is stricty within the capacity region so that the maximum weight scheduing agorithm wi stabiize the network 1]-3]. B. Backog/Deay Anaysis or i.i.d Arriva Traic In this subsection, we obtain a deay bound or the aorementioned scheduing scheme using the yapunov drit technique 1]-3]. Traic arriving to a transmitting buer o wireess ink is assumed to be i.i.d over time with average arriva rate λ. In the oowing, we use a resut which was stated in 13]. emma 1: (Theorem 1 rom 13]) et (t) be the queue backog vector in time sot t and ( (t)) be a yapunov unction. Aso, deine a one-step yapunov drit as oows: (t) = E ( (t + 1)) ( (t)) } (3) where the expectation E(.) is taken over the randomness o queue backogs (t) and system dynamics given the queue backogs (t). I the yapunov drit satisies then we have 1 t 1 im sup t t τ=0 (t) E g(t)} E (t)} (4) E (t)} im sup t 1 t 1 t τ=0 E g(t)}. (5) Now, consider the oowing quadratic yapunov unction ( (t)) = (t). (6) We have the oowing resut or the yapunov drit. Proposition 1: The yapunov drit satisies the oowing reation or any time sot t: where (t) = E B(t)} + E (t) (A (t) µ (t))} (7) B(t) = A (t) µ (t)] = A (t) + A (t)µ (t) + µ (t). (8) The proo o this proposition oows directy by appying the queue evoution reation in (1), and is omitted or brevity. As shown in 1], the capacity region coincides with the } convex hu o a possibe easibe schedues. et S = Ri be the set o a possibe schedues where one particuar schedue R i is a coumn vector o dimension with the -th eement equa 1 i ink is schedued and equa 0 otherwise. For any arriva rate vector λ stricty inside the capacity region, we have λ β iri (9) where denotes the cardinaity o set S, β i < 1 and <, denotes both a reguar inequaity and an eementwise inequaity. We have the oowing reation N λ = tr λ β i tr Ri tr µ β i < tr µ (10) where.] tr denotes the vector transposition and µ is the optima schedued vector given backog vector. It can be veriied that these resuts hod by using the reations in (9) and (). Now, we state a bound on the tota queue backogs or i.i.d. arriva traic in the oowing proposition. Proposition : Assume that the arriva rate vector λ is stricty inside the capacity region so that there exists a vector ɛ such that λ+ ɛ is inside the capacity region where ɛ is a vector with a eements equa to ɛ. Aso, assume that a arriva processes on a wireess inks have bounded second moments. Then, the network is stabe and the tota average queue backog can be bounded as + E A (t) } λ (11) ɛ where = λ is the tota ink arriva rates. Proo: Using (10) or backog vector (t), we have ] tr ] ] tr (t) λ + ɛ (t) µ (t). (1) Hence, ] tr ] tr ] tr (t) λ (t) µ (t) (t) ɛ. (13) Note that the second term o (7) can be written as E (t) (A (t) µ (t))} = E (t) (λ µ (t))} = E (t) ] tr ( λ µ(t) ) }. (14) Using (13) and (14) in (7) with µ(t) representing an optima schedued vector, we have (t) E B(t)} (t) ] tr ɛ
3 3 = E B(t)} ɛ E (t)}. (15) Using the resut in emma 1 in (15), we have im sup t 1 t 1 t τ=0 E (τ)} B ɛ (16) where B = 1 t 1 im sup t t τ=0 E B(τ)}. From (8), using the act that µ (t) 1 and arriva processes have bounded second moments, we have B <. Thereore, the queueing network is strongy stabe. Because it evoves according to an ergodic Markov chain with countabe state space, the imiting time averages o queue backogs equa to the corresponding steady state averages. To cacuate B, we note that under the stabiity condition we have 1 t 1 im sup t τ=0 µ (τ) = λ. Aso, note that µ (t) = t µ (t) because µ (t) = 0, 1} depending on whether ink is schedued in time sot t or not. As a consequence, B can be written as B = = + E A (t) } λ + λ E A (t) } λ. (17) Because time average imits o queue backogs are equa to their steady state averages, using (17) the inequaity (16) can be rewritten as + E A (t) } λ. (18) ɛ Hence, the proposition is proved. 1) Deay Bound: Appying itte s aw to (11), we can obtain a deay bound as oows: E A (t) } λ ] W (19) ɛ Now, in order to understand the scaing o this deay bound, we need to determine the reationship between the traic oading actor ρ and the parameter ɛ. et us denote by Λ the capacity region. Assume that the arriva rate vector λ = (λ1, λ,, λ ) tr is stricty inside the capacity region Λ, then there exists a oading actor ρ < 1 such that λ ρλ. (0) In the oowing, we state a deay bound by choosing a straightorward oading actor ρ as a unction o ɛ. Proposition 3: I arriva rate is in ρ-scaed capacity region as described in (0), the average tota deay can be bounded as E A (t) } ] ] λ W. (1) (1 ρ) In the specia case where the arriva process on each wireess ink is Poisson, we have W (1 1 λ ). () 1 ρ Proo: The proo oows by using the act that we can choose ɛ = (1 ρ) 1 where 1 is an a-one vector with dimension such that λ+ ɛ Λ or any λ ρλ. Speciicay, by pugging ɛ = (1 ρ) into the deay bound in (19), we can obtain (1). Now, we show that λ+ ɛ Λ or ɛ = (1 ρ). Note that or any λ ρλ, we can write λ = ρ β ir i where β i < 1. Deine e i be a vector o dimension with a zeros except a one at the i-th position. It can be easiy seen that any e i (i = 1,,, ) represents a easibe schedue (with ink i being activated). Aso, note that e i = 1. Hence, we have the oowing resut 1 ρ 1 +ρ β i Ri = 1 ρ e i +ρ β iri Λ. (3) When the arriva processes are Poisson, we have E A (t) } = λ + λ. Using this reationship in the deay bound (1), we obtain (). Note that the term 1 E E A (t) } is typicay O(1) or any traic satisying A (t) A max. In act, in such cases 1 we have E E A (t) } A max. Hence, the deay bound stated in Proposition 3 is typicay O(/(1 ρ)). C. Tighter Deay Bound In the oowing, we state a tighter deay bound under speciic assumptions which can be achieved by expoiting underying intererence constraints and network topoogy. Proposition 4: Assume that the arriva rate is in the ρ- scaed capacity region as described in (0). Aso, assume that we can ind a set o easibe schedues, namey Ψ = s i, i = 1,,, T }, satisying the oowing assumptions For any schedue s i Ψ, i ink is activated in s i then ink is not activated in any other s j Ψ or j i (i.e., any ink shoud beong to one and ony one schedue in the set Ψ). et E be the set o inks activated by a schedues in Ψ, then E = E where reca that E is the set o a network inks (i.e., the union o activated inks by a schedues covers the whoe network). et K i denote the number o activated inks in schedue s i and K min = min i K i. Then, we have the oowing deay bound E A (t) } λ ] W K min (1 ρ) /. (4) Beore proving this proposition, we note that or wireess networks such that K min = O(), proposition 4 impies that the network deay typicay scaes as O(1/(1 ρ)). This condition woud hod i the network topoogy is suicienty sparse and uniorm so that the most baanced set o schedues Ψ (i.e., amost a schedues in Ψ have the same number o activated inks in the order sense) satisies K min = O(). Note that this condition woud be satisied or most practica wireess networks because a typica schedue woud activate most inks in the network. We wi provide one such network exampe ater the proo. Proo: The proo or this proposition oows the same ine as that or proposition 3. However, a tighter deay bound
4 4 is achieved in this proposition by constructing ɛ rom the set o schedues Ψ each o which has at east K min activated inks. Now, consider the oowing inear combination o easibe schedues whose outcome ies inside the capacity region (1 ρ) T K i T j K s i + ρ β iri Λ. (5) j Thereore, the resut stated in proposition 4 oows by pugging ɛ = (1 ρ) K min into the deay bound (19). In the oowing, we provide a simpe exampe where the assumptions o the proposition hod. Exampe: Consider a grid network and one-hop (primary) intererence mode or the sake o simpicity as being shown in Fig. 1. In this igure, we aso show how to construct a set o easibe schedues Ψ that covers the whoe network graph (again, each schedue has the same ink pattern). To anayze its deay bound, assume that the size in one dimension o the grid network is H inks, then it can be veriied that = H(H+1). From the constructed set o schedues Ψ as shown in this igure, we have K min = (H + 1) H/. Thereore, using the resut in proposition 4, the deay can be bounded as H(H + 1) E A (t) } ] ] λ W (H + 1) H/ (1 ρ) E A (t) } ] ] λ (1 ρ) which scaes typicay as O(1/(1 ρ)). a time t. In order to obtain deay bound or this case, we wi use one resut proved in 13] which is stated in the oowing emma. emma : (rom section V.A o 13]) Deine C = E A (t 1)A (t)} or E 1 and C = 0 or E. For a ink, we have E (t)a (t)} E (t)} λ + C δ + σ. Now, we state deay bounds or the case o time-correated arrivas in the oowing proposition. Proposition 5: I the arriva traic is within the ρ-scaed capacity region and the assumptions in proposition 4 are satisied, then the network is stabe and the average deay can be bounded as where W B = E B + C K min (1 ρ)/. (6) E A (t) }, C = 1 E 1 C σ + δ. (7) The proo oows by using resuts in emma and Proposition 1 so it is omitted or brevity. The term 1 E E A (t) } is typicay O(1) or any traic satisying A (t) A max. In act, in such cases we have B 1 + A max. It is not very diicut to see that or E 1, we have C λ λ max where λ max < 1 is the maximum conditiona rate over a inks and states. Hence, we can obtain the oowing deay bound W 1 + A max + max E1 λ max /(σ + δ )} K min (1 ρ)/ which scaes as O(1/(1 ρ)) or K min = O(). (8) Fig. 1. Grid networks with one-hop (primary) intererence mode. D. Anaysis or Time-Correated Arrivas with Two States Here, assume that arriva process A (t) or inks is either i.i.d. or moduated by a discrete time stationary and ergodic Markov chain Z (t) having two states (i.e., states 1 and ). et σ and δ be transition probabiities rom state 1 to state and rom state to state 1, respectivey. For each ink, deine the conditiona average arriva rates λ (m) as oows: λ (m) = E A (t) Z (t) = m}. Now, et denote by E 1 E as the set o inks with timecorreated arrivas where λ (1) λ (). Aso, assume that arriva traic to any other inks in E = E E 1 is either i.i.d or time-correated with two states satisying λ (1) = λ (). Assume that the moduating Markov chains o a arriva processes are stationary so that or a inks we have E A (t)} = λ or III. ANAYSIS OF MUTIHOP FOW CASE A. System Modes and Assumptions We consider the same network mode as section II. We assume that there is set o mutihop ows F where ow F has a ixed route rom a source node s() to a destination node d(). We denote the set o inks and nodes on the route o ow as () and R(), respectivey. For simpicity, we assume that packet arrivas to source nodes o a ows are i.i.d stochastic processes. We denote the queue ength o ow at node n at the beginning o time sot t as n(t) and the number o packets arriving at the source node o ow as A s() (t). Note that data packets o any ow are deivered to the higher ayer upon reaching the destination node, so d() (t)=0. In addition, et µ n(t) be the number o packets o ow transmitted rom node n aong ink (n, m) o its route which is buered at node m i m d(). Again, we assume that µ n(t) = 1 i we activate ink (n, m) on the route o ow and µ n(t) = 0, otherwise. Given the routes or a ows, the maximum weight scheduing agorithm is used or data deivery 1]. Speciicay, the scheduing is perormed in every time sot as oows:
5 5 Each ink (n, m) inds the maximum dierentia backogs as oows: w nm (t) = max n (t) m(t) }. (9) :(n,m) () Based on cacuated ink weights, a maximum weight schedue is ound as µ (t) = argmax w nm (t)µ nm (t). (30) µ(t) S (n,m) For any schedued ink, one packet is transmitted rom the buer o the ow achieving the maximum dierentia backog. The queue evoutions can be written as n(t + 1) = n(t) µ n(t) + π n(t) (31) where this equation hods because µ n(t) = 1 ony i n(t) 1 (i.e., we do not schedue inks with empty queues). Aso, πn(t) is the number o packets arriving to queue n(t) in time sot t which can be written as A πn(t) = n (t), i n = s() µ n 1 (t), otherwise. (3) B. Backog Bound The queue backog bound is stated in the oowing proposition. The tighter backog bound wi be deveoped ater that. Proposition 6: Assume that arriva processes or a ows are i.i.d over sots and have bounded second moments. Aso, assume that arriva rate ies within the ρ-scaed capacity region. Then, 1) The tota average queue backogs can be bounded as =1 n R() n(t) θ max max (N + D). (1 ρ) where ρ is a oading actor, max = max F } (), θ max is the maximum number o ows traversing any ink in the network, N is tota number o network nodes, and D = ( ) } E A s() (t) λ + λ. (33) =1 ) For Poisson arriva process, the backog can be bounded as θ max max (N + ) F λ n(t) (1 ρ) =1 n R() where = F λ. Proo: Consider the oowing yapunov unction ( ) (t) = =1 n R() ( n (t) ) (34) where again the expectation E(.) is taken over the randomness o queue backogs (t) and system dynamics given the queue backogs (t). The yapunov drit can be written as oows: ( (t) = E n (t + 1) ) ( n (t) ) ] =1 n R() = E π n (t) µ n(t) ] (35) =1 n R() +E n(t) πn(t) µ n(t) ].(36) =1 n R() Now, consider (35) we have E π n (t) µ n(t) ] N + B 1(t) (37) =1 n R() ] where B 1 (t) = =1 E A s() (t) µ s() }. (t) This inequaity hods because we have F,s() n π n (t) µ n(t) ] 1. Now, using (3), we can manipuate (36) as oows: E n(t) πn(t) µ n(t) ] =1 n R() = µ nm(t)wnm + s() (t)λ (38) =1 where µ nm(t) corresponds to the maximum weight schedue with queue backogs (t) and w nm = max :(n,m) () n (t) m(t) ] +. Note that we have written down n(t) m(t) ] + instead o n (t) m(t) ] because inks with negative weight wi not be schedued by the maximum weight scheduing agorithm. Note that we can rewrite =1 s() (t)λ as oows: s() (t)λ = =1 =1 (n,m) () λ n (t) m(t) ] :(n,m) () λ max n (t) m(t) ] + (39). :(n,m) () Suppose that λ = (λ ) F is stricty inside the capacity region. Then, there exists a vector ɛ such that λ+ ɛ is sti inside the capacity region. This impies that there exists a vector o ink rates (µ nm ) Co(S) such that 1] (λ + ɛ) = λ + θ nm ɛ µ nm (40) :(n,m) () :(n,m) () where Co(S) represents the convex hu o a easibe ink schedues and θ nm denotes the number o ows traversing ink (n, m). Using (38), (39), (40), we can rewrite (36) as (36) µ nm(t) + λ wnm ɛ :(n,m) () ( µ nm(t) + µ nm θ nm ɛ) w nm θ nm w nm. (41)
6 6 Now, we have the oowing n(t) () (n,m) () () (n,m) () (n,m) () n (t) m(t) ] + w nm. (4) Note that a simiar bounding technique or (n,m) () n(t) used in the above inequaity has been empoyed in 16] to prove the network stabiity. We instead aim at obtaining a tight upper-bound o queue backogs as a unction o the oading actor ρ, so the yapunov drit anaysis in this paper is very dierent rom that in 16]. Using (4), we have =1 (n,m) () max =1 (n,m) () n(t) () =1 w nm = max (n,m) () w nm θ n,m w nm. (43) where max = max F } (). Using (37), (41) and (43), the yapunov drit can be bounded as (t) N + B 1 (t) ɛ max =1 n R() n(t). (44) I the arriva processes or a ows have bounded second moments then B 1 (t) is bounded. Under this condition, the yapunov drit wi be negative when the tota backog becomes arge enough. Hence, the network is stabe and the time average imits o queue backogs are equa to their steadystate averages. Aso, it is not very diicut to see that the time average imit o B 1 (t) is equa to D. Thereore, by using emma 1 and substituting time average imits o queue backogs by their steady-state averages, we have =1 n R() n max(n + D). (45) ɛ Now, to understand the scaing o this backog bound, we need to ind ɛ as a unction o the oading actor ρ as beore. Suppose arriva rate vector λ is inside the ρ-scaed capacity region, and et λ be a vector with (n, m)-th eements equa λ nm = :(n,m) () λ. Then, we have λ = ρ β iri (46) or some non-negative β i such that β i < 1. et θ max = max } θ nm where reca that θ nm is the number o ows traversing ink (n, m). We wi show that λ (1) = λ + ɛ Λ or ɛ = (1 ρ)/(θ max ). Now, et us construct a vector λ () with its (n, m)-th eements equa to () λ nm = :(n,m) () λ(1). Then, we have ( ) λ () = λ 1 ρ + θ nm θ max where ρ β iri + 1 ρ ( 1 ρ θ max θ nm ) e nm Λ (47) denotes a vector with (n, m)-th eements equa to the quantity inside the bracket. Substitute ɛ = (1 ρ)/(θ max ) into (45), we can obtain part 1) o the proposition. To prove part ) o the proposition, we need some manipuation o D or the Poisson arriva process. Speciicay, or Poisson process we have E ( A s() (t) ) } = λ + λ. Substitute this into (33), we have D = =1 λ. Pug this into the bound in part 1), we obtain part ) o the proposition. It can be shown that the average backogs derived in this proposition scae as O(N/(1 ρ)) or max = O(1). In act, using the simiar idea as that o proposition 4, a tighter backog bound can be obtained. Speciicay, i the arriva processes satisy assumptions in proposition 6 and the assumptions o proposition 4 hod, then the tota queue backogs can be bounded as =1 n R() n θ max max (N + D) K min (1 ρ)/. (48) This backog bound typicay scaes as O(N/(1 ρ)) or max = O(1) and K min = O(). REFERENCES 1]. Tassiuas and A. Ephremides, Stabiity properties o constrained queueing systems and scheduing poicies or maximum throughput in mutihop radio networks, IEEE Trans. Automatic Contro, vo. 37, no. 1, pp , Dec ] M. Neey, E. Modiano, and C. Rohrs, Power aocation and routing in mutibeam sateites with time-varying channes, IEEE/ACM Trans. Networking, vo. 11, no. 1, pp , Feb ] M. Neey, E. Modiano, and C. Rohrs, Dynamic power aocation and routing or time varying wireess networks, IEEE INFOCOM ] M. Neey, E. Modiano, and C. i, Fairness and optima stochastic contro or heterogeneous networks, IEEE INFOCOM ] E. Modiano, D. Shah, and G. Zussman, Maximizing throughput in wireess networks via gossiping, ACM SIGMETRICS ] S. Sanghavi,. Bui, and R. Srikant, Distributed ink scheduing with constant overhead, ACM SIGMETRICS 007, June ] X. in and N. Shro, The impact o imperect scheduing on cross-ayer rate contro in wireess networks, IEEE INFOCOM ] P. Charporkar, K. Kar, and S. Sarkar, Throughput guarantees through maxima scheduing in wireess networks, Aerton 005, Sept ] Y. Yi, A. Proutiere, and M. Chiang, Compexity o wireess scheduing: Impact and tradeos, ACM Mobihoc, May ] G. Gupta and N. B. Shro, Deay anaysis o scheduing poicies in wireess networks, Asiomar Conerence on Signas, Systems, and Computers, Oct ] A. Stoyar, arge deviations o queues under os scheduing agorithms, Aerton 006, Sept ] V. J. Venkataramanan and X. in, Structura properties o DP or queue-ength based wireess scheduing agorithms, Aerton 007, Sept ] M. Neey, Deay anaysis or maxima scheduing in wireess networks with bursty traic, IEEE INFOCOM ] M. Neey, Order optima deay or opportunistic scheduing in mutiuser wireess upinks and downinks, Aerton 006, Sept ] M. Neey, Deay anaysis or max weight opportunistic scheduing in wireess systems, Aerton 008, Sept ]. Bui, R. Srikant, and A. Stoyar, Nove architecture and agorithms or deay reduction in back-pressure scheduing and routing, IEEE INFOCOM 009.
Throughput Optimal Scheduling for Wireless Downlinks with Reconfiguration Delay
Throughput Optima Scheduing for Wireess Downinks with Reconfiguration Deay Vineeth Baa Sukumaran vineethbs@gmai.com Department of Avionics Indian Institute of Space Science and Technoogy. Abstract We consider
More informationDelay Analysis of Maximum Weight Scheduling in Wireless Ad Hoc Networks
Deay Anaysis o Maximum Weigh Scheduing in Wireess Ad Hoc Neworks The MIT Facuy has made his arice openy avaiabe. Pease share how his access beneis you. Your sory maers. Ciaion As Pubished Pubisher ong
More informationPower Control and Transmission Scheduling for Network Utility Maximization in Wireless Networks
ower Contro and Transmission Scheduing for Network Utiity Maximization in Wireess Networks Min Cao, Vivek Raghunathan, Stephen Hany, Vinod Sharma and. R. Kumar Abstract We consider a joint power contro
More informationA Survey on Delay-Aware Resource Control. for Wireless Systems Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning
A Survey on Deay-Aware Resource Contro 1 for Wireess Systems Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning arxiv:1110.4535v1 [cs.pf] 20 Oct 2011 Ying Cui Vincent
More informationA New Backpressure Algorithm for Joint Rate Control and Routing with Vanishing Utility Optimality Gaps and Finite Queue Lengths
A New Backpressure Agorithm or Joint Rate Contro and Routing with Vanishing Utiity Optimaity Gaps and Finite Queue Lengths Hao Yu and Michae J. Neey Abstract The backpressure agorithm has been widey used
More informationAsynchronous Control for Coupled Markov Decision Systems
INFORMATION THEORY WORKSHOP (ITW) 22 Asynchronous Contro for Couped Marov Decision Systems Michae J. Neey University of Southern Caifornia Abstract This paper considers optima contro for a coection of
More informationAn Adaptive Opportunistic Routing Scheme for Wireless Ad-hoc Networks
An Adaptive Opportunistic Routing Scheme for Wireess Ad-hoc Networks A.A. Bhorkar, M. Naghshvar, T. Javidi, and B.D. Rao Department of Eectrica Engineering, University of Caifornia San Diego, CA, 9093
More informationArbitrary Throughput Versus Complexity Tradeoffs in Wireless Networks using Graph Partitioning
University of Pennsyvania SchoaryCommons Departmenta Papers (ESE) Department of Eectrica & Systems Engineering November 2006 Arbitrary Throughput Versus Compexity Tradeoffs in Wireess Networks using Graph
More informationOptimal Distributed Scheduling under Time-varying Conditions: A Fast-CSMA Algorithm with Applications
Optima Distributed Scheduing under Time-varying Conditions: A Fast-CSMA Agorithm with Appications Bin Li and Atia Eryimaz Abstract Recenty, ow-compexity and distributed Carrier Sense Mutipe Access (CSMA)-based
More informationExploring the Throughput Boundaries of Randomized Schedulers in Wireless Networks
Exporing the Throughput Boundaries of Randomized Scheduers in Wireess Networks Bin Li and Atia Eryimaz Abstract Randomization is a powerfu and pervasive strategy for deveoping efficient and practica transmission
More informationA Brief Introduction to Markov Chains and Hidden Markov Models
A Brief Introduction to Markov Chains and Hidden Markov Modes Aen B MacKenzie Notes for December 1, 3, &8, 2015 Discrete-Time Markov Chains You may reca that when we first introduced random processes,
More informationT.C. Banwell, S. Galli. {bct, Telcordia Technologies, Inc., 445 South Street, Morristown, NJ 07960, USA
ON THE SYMMETRY OF THE POWER INE CHANNE T.C. Banwe, S. Gai {bct, sgai}@research.tecordia.com Tecordia Technoogies, Inc., 445 South Street, Morristown, NJ 07960, USA Abstract The indoor power ine network
More informationIEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 2, FEBRUARY
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 2, FEBRUARY 206 857 Optima Energy and Data Routing in Networks With Energy Cooperation Berk Gurakan, Student Member, IEEE, OmurOze,Member, IEEE,
More informationAge-based Scheduling: Improving Data Freshness for Wireless Real-Time Traffic
Age-based Scheduing: Improving Data Freshness for Wireess Rea-Time Traffic Ning Lu Department of CS Thompson Rivers University amoops, BC, Canada nu@tru.ca Bo Ji Department of CIS Tempe University Phiadephia,
More informationDistributed Cross-Layer Optimization of Wireless Sensor Networks: A Game Theoretic Approach
Distributed Cross-Layer Optimization o Wireess Sensor Networks: A Game Theoretic Approach Jun Yuan and Wei Yu Eectrica and Computer Engineering Department, University o Toronto {steveyuan, weiyu}@commutorontoca
More informationMaximizing Sum Rate and Minimizing MSE on Multiuser Downlink: Optimality, Fast Algorithms and Equivalence via Max-min SIR
1 Maximizing Sum Rate and Minimizing MSE on Mutiuser Downink: Optimaity, Fast Agorithms and Equivaence via Max-min SIR Chee Wei Tan 1,2, Mung Chiang 2 and R. Srikant 3 1 Caifornia Institute of Technoogy,
More informationSource and Relay Matrices Optimization for Multiuser Multi-Hop MIMO Relay Systems
Source and Reay Matrices Optimization for Mutiuser Muti-Hop MIMO Reay Systems Yue Rong Department of Eectrica and Computer Engineering, Curtin University, Bentey, WA 6102, Austraia Abstract In this paper,
More informationMARKOV CHAINS AND MARKOV DECISION THEORY. Contents
MARKOV CHAINS AND MARKOV DECISION THEORY ARINDRIMA DATTA Abstract. In this paper, we begin with a forma introduction to probabiity and expain the concept of random variabes and stochastic processes. After
More informationUniprocessor Feasibility of Sporadic Tasks with Constrained Deadlines is Strongly conp-complete
Uniprocessor Feasibiity of Sporadic Tasks with Constrained Deadines is Strongy conp-compete Pontus Ekberg and Wang Yi Uppsaa University, Sweden Emai: {pontus.ekberg yi}@it.uu.se Abstract Deciding the feasibiity
More informationScalable Spectrum Allocation for Large Networks Based on Sparse Optimization
Scaabe Spectrum ocation for Large Networks ased on Sparse Optimization innan Zhuang Modem R&D Lab Samsung Semiconductor, Inc. San Diego, C Dongning Guo, Ermin Wei, and Michae L. Honig Department of Eectrica
More informationSeung Jun Baek 1 and Joon-Sang Park Introduction. example, autonomous vehicles, remote surgery, and automated
Hindawi Mathematica Probems in Engineering Voume 2017, Artice ID 4362652, 15 pages https://doi.org/10.1155/2017/4362652 Research Artice Deay-Optima Scheduing for Two-Hop Reay Networks with Randomy Varying
More informationDistributed Queue-Length based Algorithms for Optimal End-to-End Throughput Allocation and Stability in Multi-hop Random Access Networks
Distribute Queue-Length base Agorithms for Optima En-to-En Throughput Aocation an Stabiity in Muti-hop Ranom Access Networks Jiaping Liu Department of Eectrica Engineering Princeton University Princeton,
More informationIterative Decoding Performance Bounds for LDPC Codes on Noisy Channels
Iterative Decoding Performance Bounds for LDPC Codes on Noisy Channes arxiv:cs/060700v1 [cs.it] 6 Ju 006 Chun-Hao Hsu and Achieas Anastasopouos Eectrica Engineering and Computer Science Department University
More informationHeavy-traffic Delay Optimality in Pull-based Load Balancing Systems: Necessary and Sufficient Conditions
Heavy-traffic Deay Optimaity in Pu-based Load Baancing Systems: Necessary and Sufficient Conditions XINGYU ZHOU, The Ohio State University JIAN TAN, The Ohio State University NSS SHROFF, The Ohio State
More informationReliability: Theory & Applications No.3, September 2006
REDUNDANCY AND RENEWAL OF SERVERS IN OPENED QUEUING NETWORKS G. Sh. Tsitsiashvii M.A. Osipova Vadivosto, Russia 1 An opened queuing networ with a redundancy and a renewa of servers is considered. To cacuate
More information<C 2 2. λ 2 l. λ 1 l 1 < C 1
Teecommunication Network Contro and Management (EE E694) Prof. A. A. Lazar Notes for the ecture of 7/Feb/95 by Huayan Wang (this document was ast LaT E X-ed on May 9,995) Queueing Primer for Muticass Optima
More informationStochastic Complement Analysis of Multi-Server Threshold Queues. with Hysteresis. Abstract
Stochastic Compement Anaysis of Muti-Server Threshod Queues with Hysteresis John C.S. Lui The Dept. of Computer Science & Engineering The Chinese University of Hong Kong Leana Goubchik Dept. of Computer
More informationTOWARDS A FRAMEWORK FOR EFFICIENT RESOURCE ALLOCATION IN WIRELESS NETWORKS: QUALITY-OF-SERVICE AND DISTRIBUTED DESIGN
TOWARDS A FRAMEWORK FOR EFFICIENT RESOURCE ALLOCATION IN WIRELESS NETWORKS: QUALITY-OF-SERVICE AND DISTRIBUTED DESIGN DISSERTATION Presented in Partia Fufiment of the Requirements for the Degree of Doctor
More informationCategories and Subject Descriptors B.7.2 [Integrated Circuits]: Design Aids Verification. General Terms Algorithms
5. oward Eicient arge-scae Perormance odeing o Integrated Circuits via uti-ode/uti-corner Sparse Regression Wangyang Zhang entor Graphics Corporation Ridder Park Drive San Jose, CA 953 wangyan@ece.cmu.edu
More informationDistributed average consensus: Beyond the realm of linearity
Distributed average consensus: Beyond the ream of inearity Usman A. Khan, Soummya Kar, and José M. F. Moura Department of Eectrica and Computer Engineering Carnegie Meon University 5 Forbes Ave, Pittsburgh,
More informationRecursive Constructions of Parallel FIFO and LIFO Queues with Switched Delay Lines
Recursive Constructions of Parae FIFO and LIFO Queues with Switched Deay Lines Po-Kai Huang, Cheng-Shang Chang, Feow, IEEE, Jay Cheng, Member, IEEE, and Duan-Shin Lee, Senior Member, IEEE Abstract One
More informationFractional Power Control for Decentralized Wireless Networks
Fractiona Power Contro for Decentraized Wireess Networks Nihar Jinda, Steven Weber, Jeffrey G. Andrews Abstract We consider a new approach to power contro in decentraized wireess networks, termed fractiona
More informationDelay Efficient Scheduling via Redundant Constraints in Multihop Networks
Delay Eicient Scheduling via Redundant Constraints in Multihop Networks Longbo Huang, Michael J. Neely Abstract We consider the problem o delay-eicient scheduling in general multihop networks. While the
More informationOn the Performance of Wireless Energy Harvesting Networks in a Boolean-Poisson Model
On the Performance of Wireess Energy Harvesting Networks in a Booean-Poisson Mode Han-Bae Kong, Ian Fint, Dusit Niyato, and Nicoas Privaut Schoo of Computer Engineering, Nanyang Technoogica University,
More informationStabilized MAX-MIN Flow Control Using PID and PII 2 Controllers
Stabiized MAX-MIN Fow Contro Using PID and PII Controers Jeong-woo Cho and Song Chong Department o Eectrica Engineering and Computer Science Korea Advanced Institute o Science and Technoogy Daejeon 5-71,
More informationA Statistical Framework for Real-time Event Detection in Power Systems
1 A Statistica Framework for Rea-time Event Detection in Power Systems Noan Uhrich, Tim Christman, Phiip Swisher, and Xichen Jiang Abstract A quickest change detection (QCD) agorithm is appied to the probem
More informationA Fictitious Time Integration Method for a One-Dimensional Hyperbolic Boundary Value Problem
Journa o mathematics and computer science 14 (15) 87-96 A Fictitious ime Integration Method or a One-Dimensiona Hyperboic Boundary Vaue Probem Mir Saad Hashemi 1,*, Maryam Sariri 1 1 Department o Mathematics,
More informationInteractive Fuzzy Programming for Two-level Nonlinear Integer Programming Problems through Genetic Algorithms
Md. Abu Kaam Azad et a./asia Paciic Management Review (5) (), 7-77 Interactive Fuzzy Programming or Two-eve Noninear Integer Programming Probems through Genetic Agorithms Abstract Md. Abu Kaam Azad a,*,
More informationMax-Weight Scheduling in Queueing Networks with. Heavy-Tailed Traffic
Max-Weight Scheduling in Queueing Networks with Heavy-Tailed Traic arxiv:1108.0370v1 [cs.ni] 1 Aug 011 Mihalis G. Markakis, Eytan H. Modiano, and John N. Tsitsiklis Abstract We consider the problem o packet
More informationProblem set 6 The Perron Frobenius theorem.
Probem set 6 The Perron Frobenius theorem. Math 22a4 Oct 2 204, Due Oct.28 In a future probem set I want to discuss some criteria which aow us to concude that that the ground state of a sef-adjoint operator
More informationA. Distribution of the test statistic
A. Distribution of the test statistic In the sequentia test, we first compute the test statistic from a mini-batch of size m. If a decision cannot be made with this statistic, we keep increasing the mini-batch
More informationImproving the Accuracy of Boolean Tomography by Exploiting Path Congestion Degrees
Improving the Accuracy of Booean Tomography by Expoiting Path Congestion Degrees Zhiyong Zhang, Gaoei Fei, Fucai Yu, Guangmin Hu Schoo of Communication and Information Engineering, University of Eectronic
More informationCS229 Lecture notes. Andrew Ng
CS229 Lecture notes Andrew Ng Part IX The EM agorithm In the previous set of notes, we taked about the EM agorithm as appied to fitting a mixture of Gaussians. In this set of notes, we give a broader view
More informationXSAT of linear CNF formulas
XSAT of inear CN formuas Bernd R. Schuh Dr. Bernd Schuh, D-50968 Kön, Germany; bernd.schuh@netcoogne.de eywords: compexity, XSAT, exact inear formua, -reguarity, -uniformity, NPcompeteness Abstract. Open
More informationFractional Power Control for Decentralized Wireless Networks
Fractiona Power Contro for Decentraized Wireess Networks Nihar Jinda, Steven Weber, Jeffrey G. Andrews Abstract arxiv:0707.0476v2 [cs.it] 28 Apr 2008 We consider a new approach to power contro in decentraized
More informationStatistical Power System Line Outage Detection Under Transient Dynamics
1 Statistica Power System Line Outage Detection Under Transient Dynamics Georgios Rovatsos, Student Member, IEEE, Xichen Jiang, Member, IEEE, Aejandro D Domínguez-García, Member, IEEE, and Venugopa V Veeravai,
More informationMATH 172: MOTIVATION FOR FOURIER SERIES: SEPARATION OF VARIABLES
MATH 172: MOTIVATION FOR FOURIER SERIES: SEPARATION OF VARIABLES Separation of variabes is a method to sove certain PDEs which have a warped product structure. First, on R n, a inear PDE of order m is
More informationc 2016 Georgios Rovatsos
c 2016 Georgios Rovatsos QUICKEST CHANGE DETECTION WITH APPLICATIONS TO LINE OUTAGE DETECTION BY GEORGIOS ROVATSOS THESIS Submitted in partia fufiment of the requirements for the degree of Master of Science
More informationASummaryofGaussianProcesses Coryn A.L. Bailer-Jones
ASummaryofGaussianProcesses Coryn A.L. Baier-Jones Cavendish Laboratory University of Cambridge caj@mrao.cam.ac.uk Introduction A genera prediction probem can be posed as foows. We consider that the variabe
More informationCentralized Coded Caching of Correlated Contents
Centraized Coded Caching of Correated Contents Qianqian Yang and Deniz Gündüz Information Processing and Communications Lab Department of Eectrica and Eectronic Engineering Imperia Coege London arxiv:1711.03798v1
More informationEfficiently Generating Random Bits from Finite State Markov Chains
1 Efficienty Generating Random Bits from Finite State Markov Chains Hongchao Zhou and Jehoshua Bruck, Feow, IEEE Abstract The probem of random number generation from an uncorreated random source (of unknown
More informationFinite Horizon Energy-Efficient Scheduling with Energy Harvesting Transmitters over Fading Channels
Finite Horizon Energy-Efficient Scheduing with Energy Harvesting Transmitters over Fading Channes arxiv:702.06390v [cs.it] 2 Feb 207 Baran Tan Bacinogu, Eif Uysa-Biyikogu, Can Emre Koksa METU, Ankara,
More informationLeader-Follower Consensus Modeling Representative Democracy
Proceedings o the Internationa Conerence o Contro, Dynamic Systems, and Robotics Ottawa, Ontario, Canada, May 7-8, 2015 Paper o. 156 Leader-Foower Consensus Modeing Representative Democracy Subhradeep
More informationFirst-Order Corrections to Gutzwiller s Trace Formula for Systems with Discrete Symmetries
c 26 Noninear Phenomena in Compex Systems First-Order Corrections to Gutzwier s Trace Formua for Systems with Discrete Symmetries Hoger Cartarius, Jörg Main, and Günter Wunner Institut für Theoretische
More informationUnconditional security of differential phase shift quantum key distribution
Unconditiona security of differentia phase shift quantum key distribution Kai Wen, Yoshihisa Yamamoto Ginzton Lab and Dept of Eectrica Engineering Stanford University Basic idea of DPS-QKD Protoco. Aice
More informationBayesian Learning. You hear a which which could equally be Thanks or Tanks, which would you go with?
Bayesian Learning A powerfu and growing approach in machine earning We use it in our own decision making a the time You hear a which which coud equay be Thanks or Tanks, which woud you go with? Combine
More informationRelated Topics Maxwell s equations, electrical eddy field, magnetic field of coils, coil, magnetic flux, induced voltage
Magnetic induction TEP Reated Topics Maxwe s equations, eectrica eddy fied, magnetic fied of cois, coi, magnetic fux, induced votage Principe A magnetic fied of variabe frequency and varying strength is
More informationMat 1501 lecture notes, penultimate installment
Mat 1501 ecture notes, penutimate instament 1. bounded variation: functions of a singe variabe optiona) I beieve that we wi not actuay use the materia in this section the point is mainy to motivate the
More informationSum Capacity and TSC Bounds in Collaborative Multi-Base Wireless Systems
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL X, NO X, DECEMBER 004 1 Sum Capacity and TSC Bounds in Coaborative Muti-Base Wireess Systems Otiia Popescu, Student Member, IEEE, and Christopher Rose, Member,
More informationA NOTE ON QUASI-STATIONARY DISTRIBUTIONS OF BIRTH-DEATH PROCESSES AND THE SIS LOGISTIC EPIDEMIC
(January 8, 2003) A NOTE ON QUASI-STATIONARY DISTRIBUTIONS OF BIRTH-DEATH PROCESSES AND THE SIS LOGISTIC EPIDEMIC DAMIAN CLANCY, University of Liverpoo PHILIP K. POLLETT, University of Queensand Abstract
More informationDelay Asymptotics with Retransmissions and Fixed Rate Codes over Erasure Channels
Deay Asymptotics with Retransmissions and Fixed Rate Codes over Erasure Channes Jian Tan, Yang Yang, Ness B. Shroff, Hesham E Gama Department of Eectrica and Computer Engineering The Ohio State University,
More informationCompetitive Diffusion in Social Networks: Quality or Seeding?
Competitive Diffusion in Socia Networks: Quaity or Seeding? Arastoo Fazei Amir Ajorou Ai Jadbabaie arxiv:1503.01220v1 [cs.gt] 4 Mar 2015 Abstract In this paper, we study a strategic mode of marketing and
More informationDuality, Polite Water-filling, and Optimization for MIMO B-MAC Interference Networks and itree Networks
Duaity, Poite Water-fiing, and Optimization for MIMO B-MAC Interference Networks and itree Networks 1 An Liu, Youjian Eugene) Liu, Haige Xiang, Wu Luo arxiv:1004.2484v3 [cs.it] 4 Feb 2014 Abstract This
More informationSimplified Algorithms for Optimizing Multiuser Multi-Hop MIMO Relay Systems
2896 IEEE TRANSACTIONS ON COMMUNICATIONS, VO. 59, NO. 10, OCTOBER 2011 Simpified Agorithms for Optimizing Mutiuser Muti-op MIMO Reay Systems Yue Rong, Senior Member, IEEE Abstract In this paper, we address
More informationAccelerated Dual Descent for Constrained Convex Network Flow Optimization
52nd IEEE Conference on Decision and Contro December 10-13, 2013. Forence, Itay Acceerated Dua Descent for Constrained Convex Networ Fow Optimization Michae Zargham, Aejandro Ribeiro, Ai Jadbabaie Abstract
More informationMaximum likelihood decoding of trellis codes in fading channels with no receiver CSI is a polynomial-complexity problem
1 Maximum ikeihood decoding of treis codes in fading channes with no receiver CSI is a poynomia-compexity probem Chun-Hao Hsu and Achieas Anastasopouos Eectrica Engineering and Computer Science Department
More informationA Fundamental Storage-Communication Tradeoff in Distributed Computing with Straggling Nodes
A Fundamenta Storage-Communication Tradeoff in Distributed Computing with Stragging odes ifa Yan, Michèe Wigger LTCI, Téécom ParisTech 75013 Paris, France Emai: {qifa.yan, michee.wigger} @teecom-paristech.fr
More informationError-free Multi-valued Broadcast and Byzantine Agreement with Optimal Communication Complexity
Error-free Muti-vaued Broadcast and Byzantine Agreement with Optima Communication Compexity Arpita Patra Department of Computer Science Aarhus University, Denmark. arpita@cs.au.dk Abstract In this paper
More informationAge of Information: The Gamma Awakening
Age of Information: The Gamma Awakening Eie Najm and Rajai Nasser LTHI, EPFL, Lausanne, Switzerand Emai: {eie.najm, rajai.nasser}@epf.ch arxiv:604.086v [cs.it] 5 Apr 06 Abstract Status update systems is
More informationEquilibrium of Heterogeneous Congestion Control Protocols
Equiibrium of Heterogeneous Congestion Contro Protocos Ao Tang Jiantao Wang Steven H. Low EAS Division, Caifornia Institute of Technoogy Mung Chiang EE Department, Princeton University Abstract When heterogeneous
More informationFast Blind Recognition of Channel Codes
Fast Bind Recognition of Channe Codes Reza Moosavi and Erik G. Larsson Linköping University Post Print N.B.: When citing this work, cite the origina artice. 213 IEEE. Persona use of this materia is permitted.
More information2M2. Fourier Series Prof Bill Lionheart
M. Fourier Series Prof Bi Lionheart 1. The Fourier series of the periodic function f(x) with period has the form f(x) = a 0 + ( a n cos πnx + b n sin πnx ). Here the rea numbers a n, b n are caed the Fourier
More informationDynamic Matching Markets and Voting Paths
Dynamic Matching Markets and Voting Paths David J. Abraham Teikepai Kavitha Abstract We consider a matching market, in which the aim is to maintain a popuar matching between a set o appicants and a set
More information1 Models of vehicles with differential constraints. 2 Traveling salesperson problems. 3 The heavy load case. 4 The light load case
Dynamic Vehice Routing for Robotic Networks Lecture #7: Vehice Modes Francesco Buo 1 Emiio Frazzoi 2 Marco Pavone 2 Ketan Sava 2 Stephen L. Smith 2 Outine of the ecture 1 Modes of vehices with differentia
More informationEfficient Anonymous Category-level Joint Tag Estimation
Eicient Anonymous Category-eve Joint Tag Estimation Min Chen Jia Liu Shigang Chen Qingjun Xiao Department o Computer & Inormation Science & Engineering University o Forida, Gainesvie, FL 3611, USA State
More informationPartial permutation decoding for MacDonald codes
Partia permutation decoding for MacDonad codes J.D. Key Department of Mathematics and Appied Mathematics University of the Western Cape 7535 Bevie, South Africa P. Seneviratne Department of Mathematics
More informationDIGITAL FILTER DESIGN OF IIR FILTERS USING REAL VALUED GENETIC ALGORITHM
DIGITAL FILTER DESIGN OF IIR FILTERS USING REAL VALUED GENETIC ALGORITHM MIKAEL NILSSON, MATTIAS DAHL AND INGVAR CLAESSON Bekinge Institute of Technoogy Department of Teecommunications and Signa Processing
More informationAn Algorithm for Pruning Redundant Modules in Min-Max Modular Network
An Agorithm for Pruning Redundant Modues in Min-Max Moduar Network Hui-Cheng Lian and Bao-Liang Lu Department of Computer Science and Engineering, Shanghai Jiao Tong University 1954 Hua Shan Rd., Shanghai
More informationSection 6: Magnetostatics
agnetic fieds in matter Section 6: agnetostatics In the previous sections we assumed that the current density J is a known function of coordinates. In the presence of matter this is not aways true. The
More informationSchedulability Analysis of Deferrable Scheduling Algorithms for Maintaining Real-Time Data Freshness
1 Scheduabiity Anaysis of Deferrabe Scheduing Agorithms for Maintaining Rea-Time Data Freshness Song Han, Deji Chen, Ming Xiong, Kam-yiu Lam, Aoysius K. Mok, Krithi Ramamritham UT Austin, Emerson Process
More informationLinear Network Coding for Multiple Groupcast Sessions: An Interference Alignment Approach
Linear Network Coding for Mutipe Groupcast Sessions: An Interference Aignment Approach Abhik Kumar Das, Siddhartha Banerjee and Sriram Vishwanath Dept. of ECE, The University of Texas at Austin, TX, USA
More informationThe Streaming-DMT of Fading Channels
The Streaming-DMT of Fading Channes Ashish Khisti Member, IEEE, and Star C. Draper Member, IEEE arxiv:30.80v3 cs.it] Aug 04 Abstract We consider the sequentia transmission of a stream of messages over
More informationStability analysis of a max-min fair Rate Control Protocol (RCP) in a small buffer regime
Stabiity anaysis of a max-min fair Rate Contro Protoco RCP) in a sma buffer regime Thomas Voice and Gaurav Raina Cambridge Consutants and IIT Madras Abstract In this note we anayse various stabiity properties
More informationMulti-server queueing systems with multiple priority classes
Muti-server queueing systems with mutipe priority casses Mor Harcho-Bater Taayui Osogami Aan Scheer-Wof Adam Wierman Abstract We present the first near-exact anaysis of an M/PH/ queue with m > 2 preemptive-resume
More informationAsymptotic Properties of a Generalized Cross Entropy Optimization Algorithm
1 Asymptotic Properties of a Generaized Cross Entropy Optimization Agorithm Zijun Wu, Michae Koonko, Institute for Appied Stochastics and Operations Research, Caustha Technica University Abstract The discrete
More informationRandom maps and attractors in random Boolean networks
LU TP 04-43 Rom maps attractors in rom Booean networks Björn Samuesson Car Troein Compex Systems Division, Department of Theoretica Physics Lund University, Sövegatan 4A, S-3 6 Lund, Sweden Dated: 005-05-07)
More informationA unified framework for design and analysis of networked and quantized control systems
1 A unified framework for design and anaysis of networked and quantized contro systems Dragan ešić and Danie Liberzon Abstract We generaize and unify a range of recent resuts in quantized contro systems
More informationRandomized Algorithms for Throughput-Optimality and Fairness in Wireless Networks
Proceedings o the 45th IEEE Conerence on Decision & Control Manchester Grand Hyatt Hotel San Diego, CA, USA, December 13-15, 2006 Randomized Algorithms or hroughput-optimality and Fairness in Wireless
More informationGokhan M. Guvensen, Member, IEEE, and Ender Ayanoglu, Fellow, IEEE. Abstract
A Generaized Framework on Beamformer esign 1 and CSI Acquisition for Singe-Carrier Massive MIMO Systems in Miimeter Wave Channes Gokhan M. Guvensen, Member, IEEE, and Ender Ayanogu, Feow, IEEE arxiv:1607.01436v1
More informationCoupling of LWR and phase transition models at boundary
Couping of LW and phase transition modes at boundary Mauro Garaveo Dipartimento di Matematica e Appicazioni, Università di Miano Bicocca, via. Cozzi 53, 20125 Miano Itay. Benedetto Piccoi Department of
More informationHomework 5 Solutions
Stat 310B/Math 230B Theory of Probabiity Homework 5 Soutions Andrea Montanari Due on 2/19/2014 Exercise [5.3.20] 1. We caim that n 2 [ E[h F n ] = 2 n i=1 A i,n h(u)du ] I Ai,n (t). (1) Indeed, integrabiity
More informationTarget Location Estimation in Wireless Sensor Networks Using Binary Data
Target Location stimation in Wireess Sensor Networks Using Binary Data Ruixin Niu and Pramod K. Varshney Department of ectrica ngineering and Computer Science Link Ha Syracuse University Syracuse, NY 344
More informationSequential Decoding of Polar Codes with Arbitrary Binary Kernel
Sequentia Decoding of Poar Codes with Arbitrary Binary Kerne Vera Miosavskaya, Peter Trifonov Saint-Petersburg State Poytechnic University Emai: veram,petert}@dcn.icc.spbstu.ru Abstract The probem of efficient
More informationEfficient Generation of Random Bits from Finite State Markov Chains
Efficient Generation of Random Bits from Finite State Markov Chains Hongchao Zhou and Jehoshua Bruck, Feow, IEEE Abstract The probem of random number generation from an uncorreated random source (of unknown
More informationLINEAR DETECTORS FOR MULTI-USER MIMO SYSTEMS WITH CORRELATED SPATIAL DIVERSITY
LINEAR DETECTORS FOR MULTI-USER MIMO SYSTEMS WITH CORRELATED SPATIAL DIVERSITY Laura Cottateucci, Raf R. Müer, and Mérouane Debbah Ist. of Teecommunications Research Dep. of Eectronics and Teecommunications
More informationTRAVEL TIME ESTIMATION FOR URBAN ROAD NETWORKS USING LOW FREQUENCY PROBE VEHICLE DATA
TRAVEL TIME ESTIMATIO FOR URBA ROAD ETWORKS USIG LOW FREQUECY PROBE VEHICLE DATA Erik Jeneius Corresponding author KTH Roya Institute of Technoogy Department of Transport Science Emai: erik.jeneius@abe.kth.se
More informationTHE THREE POINT STEINER PROBLEM ON THE FLAT TORUS: THE MINIMAL LUNE CASE
THE THREE POINT STEINER PROBLEM ON THE FLAT TORUS: THE MINIMAL LUNE CASE KATIE L. MAY AND MELISSA A. MITCHELL Abstract. We show how to identify the minima path network connecting three fixed points on
More informationAST 418/518 Instrumentation and Statistics
AST 418/518 Instrumentation and Statistics Cass Website: http://ircamera.as.arizona.edu/astr_518 Cass Texts: Practica Statistics for Astronomers, J.V. Wa, and C.R. Jenkins, Second Edition. Measuring the
More informationhttps://doi.org/ /epjconf/
HOW TO APPLY THE OPTIMAL ESTIMATION METHOD TO YOUR LIDAR MEASUREMENTS FOR IMPROVED RETRIEVALS OF TEMPERATURE AND COMPOSITION R. J. Sica 1,2,*, A. Haefee 2,1, A. Jaai 1, S. Gamage 1 and G. Farhani 1 1 Department
More informationGauss Law. 2. Gauss s Law: connects charge and field 3. Applications of Gauss s Law
Gauss Law 1. Review on 1) Couomb s Law (charge and force) 2) Eectric Fied (fied and force) 2. Gauss s Law: connects charge and fied 3. Appications of Gauss s Law Couomb s Law and Eectric Fied Couomb s
More information