22 research outputs found
Characterizing Policies with Optimal Response Time Tails under Heavy-Tailed Job Sizes
We consider the tail behavior of the response time distribution in an M/G/1 queue with heavy-tailed job sizes, specifically those with intermediately regularly varying tails. In this setting, the response time tail of many individual policies has been characterized, and it is known that policies such as Shortest Remaining Processing Time (SRPT) and Foreground-Background (FB) have response time tails of the same order as the job size tail, and thus such policies are tail-optimal. Our goal in this work is to move beyond individual policies and characterize the set of policies that are tail-optimal. Toward that end, we use the recently introduced SOAP framework to derive sufficient conditions on the form of prioritization used by a scheduling policy that ensure the policy is tail-optimal. These conditions are general and lead to new results for important policies that have previously resisted analysis, including the Gittins policy, which minimizes mean response time among policies that do not have access to job size information. As a by-product of our analysis, we derive a general upper bound for fractional moments of M/G/1 busy periods, which is of independent interest
A large-deviations analysis of the GI/GI/1 SRPT queue
We consider a GI/GI/1 queue with the shortest remaining processing time
discipline (SRPT) and light-tailed service times. Our interest is focused on
the tail behavior of the sojourn-time distribution. We obtain a general
expression for its large-deviations decay rate. The value of this decay rate
critically depends on whether there is mass in the endpoint of the service-time
distribution or not. An auxiliary priority queue, for which we obtain some new
results, plays an important role in our analysis. We apply our SRPT-results to
compare SRPT with FIFO from a large-deviations point of view.Comment: 22 page
Characterizing Policies with Optimal Response Time Tails under Heavy-Tailed Job Sizes
We consider the tail behavior of the response time distribution in an M/G/1 queue with heavy-tailed job sizes, specifically those with intermediately regularly varying tails. In this setting, the response time tail of many individual policies has been characterized, and it is known that policies such as Shortest Remaining Processing Time (SRPT) and Foreground-Background (FB) have response time tails of the same order as the job size tail, and thus such policies are tail-optimal. Our goal in this work is to move beyond individual policies and characterize the set of policies that are tail-optimal. Toward that end, we use the recently introduced SOAP framework to derive sufficient conditions on the form of prioritization used by a scheduling policy that ensure the policy is tail-optimal. These conditions are general and lead to new results for important policies that have previously resisted analysis, including the Gittins policy, which minimizes mean response time among policies that do not have access to job size information. As a by-product of our analysis, we derive a general upper bound for fractional moments of M/G/1 busy periods, which is of independent interest
Queue Length Asymptotics for Generalized Max-Weight Scheduling in the presence of Heavy-Tailed Traffic
We investigate the asymptotic behavior of the steady-state queue length
distribution under generalized max-weight 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-alpha 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 contains an intuitively surprising result - 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 max-weight-alpha 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