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22
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 waiting-time and/or sojourn-time 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 waiting-time and/or sojourn-time 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.
Analysis of multi-server 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
Veciana, “Architecture and abstractions for environment and traffic aware system-level coordination of wireless networks: The downlink case
- in INFOCOM, 2008
"... Abstract—Two ways to substantially enhance wireless broadband capacity are full frequency reuse and smaller cells, both of which result in operational regimes that are highly dynamic and interference limited. This paper presents a system-level approach to interference management, that has reasonable ..."
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Cited by 19 (4 self)
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Abstract—Two ways to substantially enhance wireless broadband capacity are full frequency reuse and smaller cells, both of which result in operational regimes that are highly dynamic and interference limited. This paper presents a system-level approach to interference management, that has reasonable backhaul communication and computation requirements. The basis for the approach is clustering and aggregation of measurements of the spatial diversity in sensitivity to interference associated with average user populations. This enables the system to exchange information and optimize coordinated transmission schedules using only coarse grained data. The paper explores various ways of optimizing such schedules: from a static, decoupled version to a dynamic version capturing user-level scheduling, fluctuating loads and inter-cell interference that couples base stations’ performance. Based on extensive system-level simulations, we demonstrate reductions in file transfer delay ranging from 20– 80%, from light to heavy loads, as compared to a simple baseline not unlike those in the field today. This improvement is achieved while providing more uniform coverage, and reducing base station power consumption by up to 45%. I.
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.
Beyond processor sharing
- SIGMETRICS Perform. Eval. Rev
"... While the (Egalitarian) Processor-Sharing (PS) discipline offers crucial insights in the performance of fair resource allocation mechanisms, it is inherently limited in analyzing and designing differentiated scheduling algorithms such as Weighted Fair Queueing and Weighted Round-Robin. The Discrimin ..."
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Cited by 8 (2 self)
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While the (Egalitarian) Processor-Sharing (PS) discipline offers crucial insights in the performance of fair resource allocation mechanisms, it is inherently limited in analyzing and designing differentiated scheduling algorithms such as Weighted Fair Queueing and Weighted Round-Robin. The Discriminatory Processor-Sharing (DPS) and Generalized Processor-Sharing (GPS) disciplines have emerged as natural generalizations for modeling the performance of such service differentiation mechanisms. A further extension of the ordinary PS policy is the Multilevel Processor-Sharing (MLPS) discipline, which has captured a pivotal role in the analysis, design and implementation of size-based scheduling strategies. We review various key results for DPS, GPS and MLPS models, highlighting to what extent these disciplines inherit desirable properties from ordinary PS or are capable of delivering service differentiation.
Queue Length Asymptotics for Generalized Max-Weight Scheduling in the presence of Heavy-Tailed Traffic
"... Abstract—We investigate the asymptotic behavior of the steady-state queue length distribution under generalized maxweight scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed tra ..."
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Cited by 6 (0 self)
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Abstract—We investigate the asymptotic behavior of the steady-state queue length distribution under generalized maxweight scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic, and the other receives light-tailed traffic. We study the class of throughput optimal max-weight-α scheduling policies, and derive an exact asymptotic characterization of the steady-state queue length distributions. In particular, we show that the tail of the light queue distribution is heavier than a power-law curve, whose tail coefficient we obtain explicitly. Our asymptotic characterization also shows that the celebrated max-weight scheduling policy leads to the worst possible tail of the light queue distribution, among all non-idling policies. Motivated by the above ‘negative ’ result regarding the maxweight-α policy, we analyze a log-max-weight (LMW) scheduling policy. We show that the LMW policy guarantees an exponentially decaying light queue tail, while still being throughput optimal. I.
When Heavy-Tailed and Light-Tailed Flows Compete: The Response Time Tail Under Generalized Max-Weight Scheduling
"... This paper focuses on the design and analysis of scheduling policies for multi-class queues, such as those found in wireless networks and high-speed switches. In this context, we study the response time tail under generalized max-weight policies in settings where the traffic flows are highly asymmet ..."
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Cited by 4 (1 self)
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This paper focuses on the design and analysis of scheduling policies for multi-class queues, such as those found in wireless networks and high-speed switches. In this context, we study the response time tail under generalized max-weight policies in settings where the traffic flows are highly asymmetric. Specifically, we study an extreme setting with two traffic flows, one heavy-tailed, and one light-tailed. In this setting, we prove that classical max-weight scheduling, which is known to be throughput optimal, results in the light-tailed flow having heavy-tailed response times. However, we show that via a careful design of inter-queue scheduling policy (from the class of generalized max-weight policies) and intra-queue scheduling policies, it is possible to maintain throughput optimality, and guarantee lighttailed delays for the light-tailed flow, without affecting the response time tail for the heavy-tailed flow.
Throughput optimal scheduling in the presence of heavy-tailed traffic
- in Proceedings of the 48th Annual Allerton Conference on Communication, Control, and Computing
, 2010
"... Abstract—We investigate the tail behavior of the steady-state queue occupancies under throughput optimal scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives traffic that is heavy-tailed (the ..."
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Cited by 3 (3 self)
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Abstract—We investigate the tail behavior of the steady-state queue occupancies under throughput optimal scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives traffic that is heavy-tailed (the “heavy queue”), and the other receives light-tailed traffic (the “light queue”). The queues are connected to the server through time-varying ON/OFF links. We study a generalized version of max-weight scheduling, called the max-weight-α policy, and show that the light queue occupancy distribution is heavy-tailed for arrival rates above a threshold value. We also obtain the exact ‘tail coefficient ’ of the light queue occupancy distribution under maxweight-alpha scheduling. Next, we show that the policy that gives complete priority to the light queue guarantees the best possible tail behavior of both queue occupancy distributions. However, the priority policy is not throughput optimal, and can cause undesirable instability effects in the heavy queue. Finally, we propose a log-max-weight (LMW) scheduling policy. We show that in addition to being throughput optimal, the LMW policy guarantees that the light queue occupancy distribution is light-tailed, for all arrival rates that the priority policy can stabilize. Thus, the LMW scheduling policy has desirable performance on both fronts, namely throughput optimality, and the tail behavior of the light queue occupancy distribution. I.
