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35
The impact of the service discipline on delay asymptotics
, 2003
"... This paper surveys the M/G/1 queue with regularly varying service requirement distribution. It studies the effect of the service discipline on the tail behavior of the waitingtime and/or sojourntime distribution, demonstrating that different disciplines lead to quite different tail behavior. The o ..."
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Cited by 30 (7 self)
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This paper surveys the M/G/1 queue with regularly varying service requirement distribution. It studies the effect of the service discipline on the tail behavior of the waitingtime and/or sojourntime distribution, demonstrating that different disciplines lead to quite different tail behavior. The orientation of the paper is methodological: We outline four different methods for determining tail behavior, illustrating them for service disciplines like FCFS, Processor Sharing and LCFS.
Large Deviation Analysis of Subexponential Waiting Times in a Processor Sharing Queue
, 2001
"... We investigate the distribution of the waiting time V in a stable M/G/1 processor sharing queue with trac intensity < 1. When the distribution of a customer service request B belongs to a large class of subexponential distributions with tails heavier than e , it is shown that P[V > x] = ..."
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Cited by 26 (5 self)
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We investigate the distribution of the waiting time V in a stable M/G/1 processor sharing queue with trac intensity < 1. When the distribution of a customer service request B belongs to a large class of subexponential distributions with tails heavier than e , it is shown that P[V > x] = P[B > (1 )x](1 + o(1)) as x !1: Furthermore, we demonstrate that the preceding relationship does not hold if the service distribution has a lighter tail than e .
Analysis of multiserver systems via dimensionality reduction of Markov chains
 School of Computer Science, Carnegie Mellon University
, 2005
"... The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chai ..."
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Cited by 22 (4 self)
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The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chains (DR). Moment matching algorithms allow us to approximate a general distribution with a phase type (PH) distribution. Our moment matching algorithms improve upon existing ones with respect to the computational efficiency (we provide closed form solutions) as well as the quality and generality of the solution (the first three moments of almost any nonnegative distribution are matched). Approximating job size and interarrival time distributions by PH distributions enables modeling a multiserver system by a Markov chain, so that the performance of the system is given by analyzing the Markov chain. However, when the multiserver system involves resource sharing or prioritization, the Markov chain often has a multidimensionally infinite state space, which makes the analysis computationally hard. DR allows us to closely approximate a multidimensionally infinite Markov chain with a Markov
The Asymptotic Workload Behavior of Two Coupled Queues
 QUEUEING SYSTEMS
, 2002
"... We consider a system of two coupled queues, Q 1 and Q 2 . When both queues are backlogged, they are each served at unit rate. However, when one queue empties, the service rate at the other queue increases. Thus, the two queues are coupled through the mechanism for dynamically sharing surplus serv ..."
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Cited by 22 (5 self)
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We consider a system of two coupled queues, Q 1 and Q 2 . When both queues are backlogged, they are each served at unit rate. However, when one queue empties, the service rate at the other queue increases. Thus, the two queues are coupled through the mechanism for dynamically sharing surplus service capacity. We derive the
Reduced Load Equivalence under Subexponentiality
, 2001
"... A+B of a queue with capacity # loaded by two independent processes A and B is investigated. When the probability of load deviation in process A decays slower than both in B and e  , we show that W A+B is asymptotically equal to the reduced load queue W A , where b is the mean rate of B. This co ..."
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Cited by 16 (3 self)
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A+B of a queue with capacity # loaded by two independent processes A and B is investigated. When the probability of load deviation in process A decays slower than both in B and e  , we show that W A+B is asymptotically equal to the reduced load queue W A , where b is the mean rate of B. This complements the known result that this property does not hold when both processes have lighter than e  deviation decay rates. Furthermore, using the same methodology, we show that under an equivalent set of conditions the results on sampling at subexponential times hold. Keywords: Large deviations, nonCramer type conditions, reduced load equivalence, independent sampling, subexponential distributions 1
Analysis of Cycle Stealing with Switching Times and Thresholds
, 2004
"... We consider two processors, each serving its own M/GI/1 queue, where one of the processors (the \donor") can help the other processor (the \beneciary") with its jobs, during times when the donor processor is idle. That is the beneciary processor \steals idle cycles " from the donor pr ..."
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Cited by 16 (4 self)
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We consider two processors, each serving its own M/GI/1 queue, where one of the processors (the \donor") can help the other processor (the \beneciary") with its jobs, during times when the donor processor is idle. That is the beneciary processor \steals idle cycles " from the donor processor. There is a switching time required for the donor processor to start working on the beneciary jobs, as well as a switching back time. We also allow for threshold constraints on both the beneciary and donor sides, whereby the decision to help is based not only on idleness but also on satisfying threshold criteria in the number of jobs. We analyze the mean response time for the donor and beneciary processors. Our analysis is approximate, but can be made as accurate as desired, and is validated via simulation. Results of the analysis illuminate principles on the general benets of cycle stealing and the design of cycle stealing policies.
Heavy tails: the effect of the service discipline
 In Computer Performance Evaluation  Modelling Techniques and Tools (TOOLS
, 2002
"... Abstract. This paper considers the M/G/1 queue with regularly varying service requirement distribution. It studies the effect of the service discipline on the tail behavior of the waiting or sojourn time distribution, demonstrating that different disciplines may lead to quite different tail behavio ..."
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Cited by 15 (2 self)
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Abstract. This paper considers the M/G/1 queue with regularly varying service requirement distribution. It studies the effect of the service discipline on the tail behavior of the waiting or sojourn time distribution, demonstrating that different disciplines may lead to quite different tail behavior. The orientation of the paper is methodological: We outline three different methods of determining tail behavior, illustrating them for service disciplines like FCFS, Processor Sharing and LCFS. This paper is dedicated to the memory of Vincent Dumas, a dear friend and gifted young mathematician. 1
Analysis of Cycle Stealing with Switching Cost
, 2003
"... We analyze the mean response time for the donor and beneficiary processors. Our analysis is approximate, but can be made as accurate as desired, and is validated via simulation. Results of the analysis illuminate several interesting principles with respect to the general benefits of cycle stealing a ..."
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Cited by 13 (11 self)
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We analyze the mean response time for the donor and beneficiary processors. Our analysis is approximate, but can be made as accurate as desired, and is validated via simulation. Results of the analysis illuminate several interesting principles with respect to the general benefits of cycle stealing and the design of cycle stealing policies.
Generalized Processor Sharing Queues With Heterogeneous Traffic Classes
, 2001
"... We consider a queue fed by a mixture of lighttailed and heavytailed traffic. The two traffic flows are served in accordance with the Generalized Processor Sharing (GPS) discipline. GPSbased scheduling algorithms, such as Weighted Fair Queueing (WFQ), have emerged as an important mechanism for ach ..."
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Cited by 11 (7 self)
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We consider a queue fed by a mixture of lighttailed and heavytailed traffic. The two traffic flows are served in accordance with the Generalized Processor Sharing (GPS) discipline. GPSbased scheduling algorithms, such as Weighted Fair Queueing (WFQ), have emerged as an important mechanism for achieving service differentiation in integrated networks. We derive the asymptotic workload behavior of the lighttailed traffic flow under the assumption that its GPS weight is larger than its traffic intensity. The GPS mechanism ensures that the workload is bounded above by that in an isolated system with the lighttailed flow served in isolation at a constant rate equal to its GPS weight. We show that the workload distribution is in fact asymptotically equivalent to that in the isolated system, multiplied with a certain prefactor, which accounts for the interaction with the heavytailed flow. Specifically, the prefactor represents the probability that the heavytailed flow is backlogged long enough for the lighttailed flow to reach overflow. The results provide crucial qualitative insight in the typical overflow scenario.