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On Throughput Optimality with Delayed NetworkState Information
, 2008
"... We study the problem of routing/scheduling in a wireless network with partial/delayed Network (channel and queue) State Information (NSI). We consider two cases: (i) centralized routing/scheduling, where a central controller obtains heterogeneous delayed information from each of the nodes (thus, the ..."
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We study the problem of routing/scheduling in a wireless network with partial/delayed Network (channel and queue) State Information (NSI). We consider two cases: (i) centralized routing/scheduling, where a central controller obtains heterogeneous delayed information from each of the nodes (thus, the controller has NSI with different delays from different nodes), and makes the routing/scheduling decisions; (ii) decentralized routing/scheduling, where each node makes a decision based on its current channel and queue states along with homogeneous delayed NSI from other nodes. For each of the cases (with additional flow restrictions for the decentralized routing/scheduling case), we first characterize the optimal network throughput regions under the above described NSI models and show that the throughput regions shrinks with the increase of delay. Further, we propose channel and queue length based routing/scheduling algorithms that achieve the above throughput regions.
A multiclass queue in heavy traffic with throughput time constraints: Asymptotically optimal dynamic controls. Queueing Syst
 Theory Appl
, 2001
"... Abstract. Consider a singleserver queueing system with K job classes, each having its own renewal input process and its own general service time distribution. Further suppose the queue is in heavy traffic, meaning that its traffic intensity parameter is near the critical value of one. A system mana ..."
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Abstract. Consider a singleserver queueing system with K job classes, each having its own renewal input process and its own general service time distribution. Further suppose the queue is in heavy traffic, meaning that its traffic intensity parameter is near the critical value of one. A system manager must decide whether or not to accept new jobs as they arrive, and also the order in which to serve jobs that are accepted. The goal is to minimize penalties associated with rejected jobs, subject to upper bound constraints on the throughput times for accepted jobs; both the penalty for rejecting a job and the bound on the throughput time may depend on job class. This problem formulation does not make sense in a conventional queueing model, because throughput times are random variables, but we show that the formulation is meaningful in an asymptotic sense, as one approaches the heavy traffic limit under diffusion scaling. Moreover, using a method developed recently by Bramson and Williams, we prove that a relatively simple dynamic control policy is asymptotically optimal in this framework. Our proposed policy rejects jobs from one particular class when the server’s nominal workload is above a threshold value, accepting all other arrivals; and the sequencing rule for accepted jobs is one that maintains near equality of the relative backlogs for different classes, defined in a natural sense. 1. Introduction and
Delay considerations for opportunistic scheduling in broadcast fading channels
 IEEE Trans. Wireless Commun
, 2007
"... We consider a singleantenna broadcast block fading channel with users where the transmission is packetbased. We define the (packet) delay as the minimum number of channel uses that guarantees all users successfully receive packets. This is a more stringent notion of delay than average delay and is ..."
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We consider a singleantenna broadcast block fading channel with users where the transmission is packetbased. We define the (packet) delay as the minimum number of channel uses that guarantees all users successfully receive packets. This is a more stringent notion of delay than average delay and is the worst case (access) delay among the users. A delay optimal scheduling scheme, such as roundrobin, achieves the delay of. For the opportunistic scheduling (which is throughput optimal) where the transmitter sends the packet to the user with the best channel conditions at each channel use, we derive the mean and variance of the delay for any and. For large and in a homogeneous network, it is proved that the expected delay in receiving one packet by all the receivers scales as, as opposed to for the roundrobin scheduling. We also show that when grows faster than, for some, then the delay scales as. This roughly determines the timescale required for the system to behave fairly in a homogeneous network. We then propose a scheme to significantly reduce the delay at the expense of a small throughput hit. We further look into the advantage of multiple transmit antennas on the delay. For a system with antennas in the transmitter where at each channel use packets are sent to different users, we obtain the expected delay in receiving one packet by all the users. Index terms: broadcast channel, fading, opportunistic scheduling, packet delay, longest queue. 1
2006), ChannelAware Earliest Deadline Due Fair Scheduling for Wireless Multimedia Networks
 Wireless Personal Communications
"... Abstract. Providing delay guarantees to timesensitive traffic in wireless multimedia networks is a challenging issue. This is due to the timevarying link capacities and the variety of realtime applications expected to be handled by such networks. We propose and evaluate the performance of a chann ..."
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Abstract. Providing delay guarantees to timesensitive traffic in wireless multimedia networks is a challenging issue. This is due to the timevarying link capacities and the variety of realtime applications expected to be handled by such networks. We propose and evaluate the performance of a channelaware scheduling discipline and a set of policies that are capable of providing such delay guarantees in TDMbased wireless networks. First, we introduce the ChannelDependent EarliestDueDate (CDEDD) discipline. In this discipline, the expiration time of the head of line packets of users ’ queues is taken into consideration in conjunction with the current channel states of users in the scheduling decision. This scheme attempts to guarantee the targeted delay bounds in addition to exploiting multiuser diversity to make best utilization of the variable capacity of the channel. We also propose the violationfair policy that can be integrated with the CDEDD discipline and two other wellknown scheduling disciplines [1, 2]. In this policy, we attempt to ensure that the number of packets dropped due to deadline violation is fairly distributed among the users. The proposed schemes can provide statistical guarantees on delays, achieve high throughput, and exhibit good fairness performance with respect to throughput and deadline violations. We provide extensive simulation results to study the performance the proposed schemes and compare them with two of the best known scheduling disciplines [1, 2] in the literature.
Channelquality dependent earliest deadline due fair scheduling schemes for wireless multimedia networks
 in Proceedings of the 7th ACM International Workshop on Modeling, Analysis and Simulation of Wireless and Mobile Systems
"... Providing delay guarantees to timesensitive traffic in wireless multimedia networks is a challenging issue. This is due to the timevarying link capacities and the variety of realtime applications expected to be handled by such networks. We propose and evaluate the performance of two channelaware ..."
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Providing delay guarantees to timesensitive traffic in wireless multimedia networks is a challenging issue. This is due to the timevarying link capacities and the variety of realtime applications expected to be handled by such networks. We propose and evaluate the performance of two channelaware scheduling schemes that are capable of providing such delay guarantees in wireless networks. In the first proposed scheme, the ChannelDependent EarliestDueDate (CDEDD) discipline, the expiration time of the head of line packets of users ' queues is taken into consideration in conjunction with the current channel states of users in the scheduling decision. This policy attempts to guarantee the targeted delay bounds in addition to exploiting multiuser diversity to make best utilization of the variable capacity of the channel. In the second scheme we attempt to ensure that the number of packets dropped due to deadline violation is fairly disturbed among users. This provides fairness in the quality of service (QoS) delivered to different users. A unique feature of our work is explicit provisioning of statistical QoS as well as ensuring fairness in data rates, delay bound, and delay bound violation. We provide extensive simulation results to show the different performance aspects of the proposed schemes.
Sojourn time tails in the M/D/1 processor sharing queue
"... We consider the sojourn time V in the MIDl1 processor sharing (PS) queue, and show that P(V> x) is of the form Ce'x as x becomes large. The proof involves a geometric random sum representation of V, and a connection with Yule processes, which also enables us to simplify Ott's (1984) de ..."
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Cited by 8 (2 self)
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We consider the sojourn time V in the MIDl1 processor sharing (PS) queue, and show that P(V> x) is of the form Ce'x as x becomes large. The proof involves a geometric random sum representation of V, and a connection with Yule processes, which also enables us to simplify Ott's (1984) derivation of the Laplace transform of V. Numerical experiments show that the approximation P(V> x) ~ Ce'x is excellent even for moderate values of x.
UserLevel QoS and Traffic Engineering for 3G Wireless 1xEVDO Systems
"... Abstract 3G wireless systems such as 3G1X, 1xEVDO and 1xEVDV provide support for a variety of highspeed data applications. The success of these services critically relies on the capability to ensure an adequate QoS experience to users at an affordable price. With wireless bandwidth at a premiu ..."
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Abstract 3G wireless systems such as 3G1X, 1xEVDO and 1xEVDV provide support for a variety of highspeed data applications. The success of these services critically relies on the capability to ensure an adequate QoS experience to users at an affordable price. With wireless bandwidth at a premium, traffic engineering and network planning play a vital role in addressing these challenges. We present models and techniques that we have developed for quantifying the QoS perception of 1xEVDO users generating FTP or Web browsing sessions. We show how userlevel QoS measures may be evaluated by means of a ProcessorSharing model which explicitly accounts for the throughput gains from multiuser scheduling. The model provides simple analytical formulas for key performance metrics such as response times, blocking probabilities and throughput. Analytical models are especially useful for network deployment and inservice tuning purposes due to the intrinsic difficulties associated with simulationbased optimization approaches. We discuss the application of our results in the context of Ocelot, which is a Lucent tool for wireless network planning and optimization. Keywords Highspeed wireless data, userlevel QoS, network optimization, blocking performance, throughput performance,
Large deviations of queues under QoS scheduling algorithms,” Allerton 2006
, 2006
"... Abstract — We consider a model where multiple queues are served by a server whose capacity varies randomly and asynchronously with respect to different queues. The problem is to optimally control large deviations of the queues in the following sense: find a scheduling rule maximizing ..."
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Cited by 7 (0 self)
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Abstract — We consider a model where multiple queues are served by a server whose capacity varies randomly and asynchronously with respect to different queues. The problem is to optimally control large deviations of the queues in the following sense: find a scheduling rule maximizing
Large deviations of maxweight scheduling policies on convex rate regions
, 2007
"... Abstract—We consider a single server discretetime system with K users where the server picks operating points from a compact, convex and coordinate convex set in ℜ K +. For this system we analyse the performance of a stablising policy that at any given time picks operating points from the allowed ..."
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Abstract—We consider a single server discretetime system with K users where the server picks operating points from a compact, convex and coordinate convex set in ℜ K +. For this system we analyse the performance of a stablising policy that at any given time picks operating points from the allowed rate region that maximise a weighted sum of rate, where the weights depend upon the workloads of the users. Assuming a Large Deviations Principle (LDP) for the arrival processes in the Skorohod space of functions that are rightcontinuous with lefthand limits we establish an LDP for the workload process using a generalised version of the contraction principle to derive the corresponding rate function. With the LDP result available we then analyse the tail probabilities of the workloads under different buffering scenarios. I.
Tailrobust Scheduling via Limited Processor Sharing
 PERFORMANCE EVALUATION
, 2010
"... From a rare events perspective, scheduling disciplines that work well under light (exponential) tailed workload distributions do not perform well under heavy (power) tailed workload distributions, and viceversa, leading to fundamental problems in designing schedulers that are robust to distribution ..."
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Cited by 7 (2 self)
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From a rare events perspective, scheduling disciplines that work well under light (exponential) tailed workload distributions do not perform well under heavy (power) tailed workload distributions, and viceversa, leading to fundamental problems in designing schedulers that are robust to distributional assumptions on the job sizes. This paper shows how to exploit partial workload information (system load) to design a scheduler that provides robust performance across heavytailed and lighttailed workloads. Specifically, we derive new asymptotics for the tail of the stationary sojourn time under Limited Processor Sharing (LPS) scheduling for both heavytailed and lighttailed job size distributions, and show that LPS can be robust to the tail of the job size distribution if the multiprogramming level is chosen carefully as a function of the load.