Results 1  10
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18
InterClass Resource Sharing using Statistical Service Envelopes
 In Proceedings of IEEE Infocom '99
, 1999
"... Networks that support multiple services through "linksharing" must address the fundamental conflicting requirement between isolation among service classes to satisfy each class' quality of service requirements, and statistical sharing of resources for efficient network utilization. ..."
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Cited by 57 (12 self)
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Networks that support multiple services through "linksharing" must address the fundamental conflicting requirement between isolation among service classes to satisfy each class' quality of service requirements, and statistical sharing of resources for efficient network utilization. While a number of service disciplines have been devised which provide mechanisms to both isolate flows and fairly share excess capacity, admission control algorithms are needed which exploit the effects of interclass resource sharing. In this paper, we develop a framework of using statistical service envelopes to study interclass statistical resource sharing. We show how this service envelope enables a class to overbook resources beyond its deterministically guaranteed capacity by statistically characterizing the excess service available due to fluctuating demands of other service classes. We apply our techniques to several multiclass schedulers, including Generalized Processor Sharing, and des...
A Mathematical Framework for Designing a LowLoss, LowDelay Internet
 Network and Spatial Economics
, 2003
"... We survey some recent results on modeling, analysis and design of congestion control schemes for the Internet. Using tools from convex optimization and control theory, we show that congestion controllers can be viewed as distributed algorithms for achieving fair resource allocation among competin ..."
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Cited by 54 (7 self)
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We survey some recent results on modeling, analysis and design of congestion control schemes for the Internet. Using tools from convex optimization and control theory, we show that congestion controllers can be viewed as distributed algorithms for achieving fair resource allocation among competing sources. We illustrate the use of simple mathematical models to analyze the behavior of currently deployed Internet congestion control protocols as well as to design new protocols for networks with large capacities, delays and general topology. These new protocols are designed to nearly eliminate loss and queueing delay in the Internet, yet achieving high utilization and any desired fairness.
OFDM Downlink Scheduling for DelayOptimality: ManyChannel ManySource Asymptotics with General Arrival Processes,” Purdue University,
, 2011
"... AbstractWe consider the downlink of an OFDM system for supporting a large number of delaysensitive users. The OFDM scheduling problem can be modeled as a discretetime multisource multiserver queuing system with timevarying connectivity. For such a system, the MaxWeight policy is known to be t ..."
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Cited by 5 (2 self)
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AbstractWe consider the downlink of an OFDM system for supporting a large number of delaysensitive users. The OFDM scheduling problem can be modeled as a discretetime multisource multiserver queuing system with timevarying connectivity. For such a system, the MaxWeight policy is known to be throughputoptimal and the ServerSide Greedy (SSG) policy has been recently shown to achieve small queue lengths for i.i.d. arrival processes. However, there is often significant difference between queuelength optimality and delay optimality, and there exist arrival patterns such that algorithms with small queue backlog can still lead to large delay. In this work, we propose a new OFDM scheduling algorithm that gives preference to packets with large delay. Assuming ONOFF channels, we show that for a large class of arrival processes, the proposed policy is ratefunction delayoptimal. We substantiate the result via both analysis and simulation.
ManySources Large Deviations for MaxWeight Scheduling
"... Abstract—In this paper, we establish a manysources large deviations principle (LDP) for the stationary workload of a multiqueue singleserver system with simplex capacity, operated under a stabilizing and nonidling maximumweight scheduling policy. Assuming a manysources sample path LDP for the ..."
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Cited by 3 (1 self)
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Abstract—In this paper, we establish a manysources large deviations principle (LDP) for the stationary workload of a multiqueue singleserver system with simplex capacity, operated under a stabilizing and nonidling maximumweight scheduling policy. Assuming a manysources sample path LDP for the arrival processes, we establish an LDP for the workload process by employing Garcia’s extended contraction principle that is applicable to quasicontinuous mappings. The LDP result can be used to calculate asymptotic buffer overflow probabilities accounting for the multiplexing gain, when the arrival process is an average of i.i.d. processes. We express the rate function for the stationary workloads in term of the rate functions of the finitehorizon workloads when the arrival processes have i.i.d. increments. I.
Priority queueing systems: from probability generating functions to tail probabilities
"... Obtaining (tail) probabilities from a transform function is an important topic in queueing theory. To obtain these probabilities in discretetime queueing systems, we have to invert probability generating functions, since most important distributions in discretetime queueing systems can be determin ..."
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Obtaining (tail) probabilities from a transform function is an important topic in queueing theory. To obtain these probabilities in discretetime queueing systems, we have to invert probability generating functions, since most important distributions in discretetime queueing systems can be determined in the form of probability generating functions. In this paper, we calculate the tail probabilities of two particular random variables in discretetime priority queueing systems, by means of the dominant singularity approximation. We show that obtaining these tail probabilities can be a complex task, and that the obtained tail probabilities are not necessarily exponential (as in most ’traditional ’ queueing systems). Further, we show the impact and significance of the various system parameters on the type of tail behavior. Finally, we compare our approximation results with simulations.
On the impact of finite buffers on perflow delays in fifo queues
 In Proc. of ITC
, 2012
"... Abstract—The literature on queueing systems with finite buffers addresses mostly asymptotic performance metrics on an aggregate flow, and/or generally relies on a convenient, but provably inaccurate, approximation of the loss probability by the overflow probability in an infinite size buffer. This p ..."
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Abstract—The literature on queueing systems with finite buffers addresses mostly asymptotic performance metrics on an aggregate flow, and/or generally relies on a convenient, but provably inaccurate, approximation of the loss probability by the overflow probability in an infinite size buffer. This paper addresses nonasymptotic perflow metrics in a multiflow queueing system with finite buffer and FIFO scheduling. The analysis dispenses with the above approximation, and lends itself to several interesting insights on the impact of finite buffers on perflow metrics. Counterintuitively, the perflow delay distribution is not monotonous in the buffer size, and such an effect is especially visible in high burstiness regimes. Another observation is that buffer dimensioning becomes insensitive to the type of SLA constraint, e.g., fixed violation probability on either loss or delay, in high multiplexing regimes. In the particular case of aggregate scheduling, the results on the aggregate input flow significantly improve upon existing results by capturing the manifestation of bufferless multiplexing in regimes with many flows. I.
Providing Qos In Large Networks: Statistical Multiplexing And Admission Control
"... In this paper we consider the problem of providing statistical Quality of Service (QoS) guarantees defined in terms of packet loss when independent heterogeneous tra#c streams access a network router of high capacity. By using a scaling technique we show how this problem becomes tractable when the s ..."
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In this paper we consider the problem of providing statistical Quality of Service (QoS) guarantees defined in terms of packet loss when independent heterogeneous tra#c streams access a network router of high capacity. By using a scaling technique we show how this problem becomes tractable when the server capacity is large and many tra#c streams are present. In particular we show that we can define an e#ective bandwidth for the sources that allows us to map the model onto a multirate loss model. In particular we show several insights on the multiplexing problem as the capacity becomes large. We also provide numerical and simulation evidence to show how the largeness of networks can be used to advantage in providing very simple admission control schemes. The techniques are based on large deviations, local limit theorems, and the productform associated with coordinate convex policies.
Asymptotic Evaluation of Delay in the SRPT Scheduler
"... In this paper, we consider the ShortestRemainingProcessingTime (SRPT) scheduling algorithm. We consider the SRPT scheduling rule for a discretetime queueing system that is accessed by a large number of flows (a many flows regime). In such an asymptotic regime (large capacity and large number of ..."
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In this paper, we consider the ShortestRemainingProcessingTime (SRPT) scheduling algorithm. We consider the SRPT scheduling rule for a discretetime queueing system that is accessed by a large number of flows (a many flows regime). In such an asymptotic regime (large capacity and large number of flows), we derive expressions for the packet delay distributions for batch arrival processes, and with bounded packet sizes. Using these results, we compare the delay asymptote (i.e., for any finite delay, and asymptotic in the number of flows) of the SRPT scheduler with that of a FIFO (FirstInFirstOut) scheduler, when there is a mix of packet sizes. Our analysis holds for any finite mix of packet sizes. We apply the result to a system accessed by packets which are one of two sizes: 1 or M, and the arrival process is i.i.d. across flows. We show that the difference in rate function of the delay asymptote between SRPT and FIFO for the size M packet decays as O ( 1 M γ) for any 0 < γ < 1 and M sufficiently large. Thus, for large packets, the delay distributions under FIFO and SRPT look similar. On the other hand, for the size 1 packet, the delay rate function under SRPT is invariant with M. However for FIFO, the delay rate function for the size 1 packet decays as O ( 1 M γ) for any 0 < γ < 1 and M large. This shows that for size 1 packets, SRPT performs increasingly better as the range in packet size increases. Thus, these results indicate that SRPT is a good policy to implement for webservers, where empirical evidence suggests a large variability in packet sizes.
On the elasticity of marking functions: Scheduling, stability, qualityofservice in the internet
, 2004
"... Abstract — Much of the research on Internet modeling and analysis has focused on the design of end controllers and network algorithms with the objective of stability and convergence of the transmission rate. However, the Internet is composed of a mixture of both (controlled) elastic flows and (unco ..."
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Abstract — Much of the research on Internet modeling and analysis has focused on the design of end controllers and network algorithms with the objective of stability and convergence of the transmission rate. However, the Internet is composed of a mixture of both (controlled) elastic flows and (uncontrolled) realtime flows. Uncontrolled realtime flows do not react to network congestion as well as they require a certain level of QoS guarantees. In this paper, we study the effects of marking elasticity (which characterizes how quickly the marking level changes during transients) on the QoS for uncontrolled realtime flows, at a router accessed by both uncontrolled realtime and controlled flows. First, we derive lower and upper bounds on the queue overflow probability at a router of a single bottleneck system. Using this, we quantify the tradeoff between stability for controlled flows and QoS guarantee for uncontrolled realtime flows as a function of marking elasticity. The results indicate that some marking functions may be “uniformly ” better than others. In particular, among the marking functions that we have compared, our bounds indicate that a rate based version of REM seems to provide the largest localstability region for any given QoS requirement. Next, as a function of the marking function elasticity, we quantify the excess capacity required at the router with FIFO scheduling that results in the same queue overflow probability if priority scheduling was used instead. We show that the difference in the required capacities with FIFO and priority queueing decreases with more elastic marking functions. In other words, the gains due to scheduling decreases with increasing marking elasticity. I.