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14
Scheduling Policies for Single-Hop Networks with Heavy-Tailed Traffic
"... Abstract—In the first part of the paper, we study the impact of scheduling, in a setting of parallel queues with a mix of heavy-tailed and light-tailed traffic. We analyze queue-length unaware scheduling policies, such as round-robin, randomized, and priority, and characterize their performance. We ..."
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Abstract—In the first part of the paper, we study the impact of scheduling, in a setting of parallel queues with a mix of heavy-tailed and light-tailed traffic. We analyze queue-length unaware scheduling policies, such as round-robin, randomized, and priority, and characterize their performance. We prove the queue-length instability of Max-Weight scheduling, in the presence of heavy-tailed traffic. Motivated by this, we analyze the performance of Max-Weight-α scheduling, and establish conditions on the α-parameters, under which the system is queue-length stable. We also introduce the Max-Weight-log policy, which provides performance guarantees, without any knowledge of the arriving traffic. In the second part of the paper, we extend the results on Max-Weight and Max-Weightα scheduling to a single-hop network, with arbitrary topology and scheduling constraints. I.
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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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.
Lookahead Actions in Dispatching to Parallel Queues
"... Applying the first policy iteration (FPI) to any static dispatching (task assignment) policy yields a new improved dynamic policy that takes into account the particular cost structure and the expected future arrivals. However, it is generally hard to go beyond that due to the complex state space and ..."
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Cited by 4 (2 self)
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Applying the first policy iteration (FPI) to any static dispatching (task assignment) policy yields a new improved dynamic policy that takes into account the particular cost structure and the expected future arrivals. However, it is generally hard to go beyond that due to the complex state space and the resulting difficulty in computing the value function for a dynamic policy. For example, applying FPI to identical FCFS servers with Bernoulli split gives the Least-Work-Left (LWL) policy, for which no closed-form value function is known. In fact, LWL with identical servers is equivalent to an M/G/k queue, the performance measures of which have remained as open problems. The situation gets even more complicated with heterogeneous servers. In this paper, we take an intermediate approach and consider lookahead actions that concern not only the current job but also the job arriving next, after which a basic (static) policy is assumed to take over. This is important as the benefits from some decisions can only be reaped with appropriate subsequent actions. The lookahead enables sound estimates also for marginal admission costs, e.g., with respect to LWL. The superior performance of the new near-optimal dispatching policies is demonstrated numerically.
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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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.
Control of parallel non-observable queues: asymptotic equivalence and optimality of periodic policies
, 2015
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Not Always a Win
"... Mor Harchol-Balter and Alan Scheller-Wolf and Andrew Young Abstract — This paper investigates the performance of task assignment policies for server farms as the variability of job sizes (service demands) approaches infinity. The Size-Interval-Task-Assignment policy (SITA), which separates short job ..."
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Mor Harchol-Balter and Alan Scheller-Wolf and Andrew Young Abstract — This paper investigates the performance of task assignment policies for server farms as the variability of job sizes (service demands) approaches infinity. The Size-Interval-Task-Assignment policy (SITA), which separates short jobs from long jobs, has long been viewed as the panacea for dealing with high-variability job-size distributions. A very recent paper [16] showed that this common wisdom is flawed: SITA can actually be inferior to the much simpler greedy policy, Least-Work-Left (LWL), for certain common job-size distributions, including many modal, hyperexponential, and Pareto distributions. The above finding leads one to question whether providing isolation for short jobs from long ones is inherently bad, or whether it is just SITA’s strict isolation of short jobs that
Task Assignment in a Server Farm with Switching Delays and General Energy-Aware Cost Structure
"... We consider the task assignment problem to parallel servers with switching delay,whereserverscanbeswitchedofftosaveenergy. However,switchingaserver back on involves a constant server-specific delay. We will use one step of policy iterationfrom astartingpolicy such asBernoullisplitting, in orderto de ..."
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We consider the task assignment problem to parallel servers with switching delay,whereserverscanbeswitchedofftosaveenergy. However,switchingaserver back on involves a constant server-specific delay. We will use one step of policy iterationfrom astartingpolicy such asBernoullisplitting, in orderto deriveefficient task assignment (dispatching) policies that minimize the long-run average cost. To evaluate our starting policy, we first analyze a single work-conserving M/G/1 queue with a switching delay and derive a value function with respect to a general cost structure. Our costs include energy related switching and running costs, as well as performance-related costs associated with both means and variability of waiting time and latency. The efficiency of our dispatching policies is illustrated with numerical examples.
Why Segregating Short Jobs from Long Jobs under High Variability is Not Always a Win
"... Abstract — This paper investigates the performance of task assignment policies for server farms as the variability of job sizes (service demands) approaches infinity. The Size-Interval-Task-Assignment policy (SITA), which separates short jobs from long jobs, has long been viewed as the panacea for d ..."
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Abstract — This paper investigates the performance of task assignment policies for server farms as the variability of job sizes (service demands) approaches infinity. The Size-Interval-Task-Assignment policy (SITA), which separates short jobs from long jobs, has long been viewed as the panacea for dealing with high-variability job-size distributions. A very recent paper [16] showed that this common wisdom is flawed: SITA can actually be inferior to the much simpler greedy policy, Least-Work-Left (LWL), for certain common job-size distributions, including many modal, hyperexponential, and Pareto distributions. The above finding leads one to question whether providing isolation for short jobs from long ones is inherently bad, or whether it is just SITA’s strict isolation of short jobs that sometimes leads to poor performance. To answer this question, we consider a much more flexible policy, which we call “Cycle-Stealing ” (CS). The CS policy is very similar to LWL, in that short jobs can go to any queue, but it still provides short jobs isolation from longs (one server is reserved for short jobs). While CS has many of the same properties as LWL, including high utilization of both servers, we prove, surprisingly, that, for high variability job sizes, CS performs poorly whenever SITA performs poorly. This result suggests that the notion of isolating short jobs from long jobs, under high variability workloads, is sometimes simply not the right thing to do. A. Task assignment policies I.
Analytic Modeling
, 2009
"... 2. Hand in Part II of the Entrance Exam by 4 p.m. tomorrow. 3. Check the class website daily. Homework 1 may go up as early as this Friday. 4. Remember that there are recitations on Friday (same room and time) to help you! Occasionally I will take over the Friday recitation to teach a missed class. ..."
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2. Hand in Part II of the Entrance Exam by 4 p.m. tomorrow. 3. Check the class website daily. Homework 1 may go up as early as this Friday. 4. Remember that there are recitations on Friday (same room and time) to help you! Occasionally I will take over the Friday recitation to teach a missed class. 5. There is a handout (typically 20 pages) for each lecture. Get into the habit now of spending at least 3 hours going over each such handout.
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"... Open-loop control of exponential queues in infinite dimension ..."
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