46 research outputs found
Shot-noise queueing models
We provide a survey of so-called shot-noise queues: queueing models with the special feature that the server speed is proportional to the amount of work it faces. Several results are derived for the workload in an M/G/1 shot-noise queue and some of its variants. Furthermore, we give some attention to queues with general workload-dependent service speed. We also discuss linear stochastic fluid networks, and queues in which the input process is a shot-noise process
Performance of the Gittins Policy in the G/G/1 and G/G/k, With and Without Setup Times
How should we schedule jobs to minimize mean queue length? In the preemptive
M/G/1 queue, we know the optimal policy is the Gittins policy, which uses any
available information about jobs' remaining service times to dynamically
prioritize jobs. For models more complex than the M/G/1, optimal scheduling is
generally intractable. This leads us to ask: beyond the M/G/1, does Gittins
still perform well?
Recent results indicate that Gittins performs well in the M/G/k, meaning that
its additive suboptimality gap is bounded by an expression which is negligible
in heavy traffic. But allowing multiple servers is just one way to extend the
M/G/1, and most other extensions remain open. Does Gittins still perform well
with non-Poisson arrival processes? Or if servers require setup times when
transitioning from idle to busy?
In this paper, we give the first analysis of the Gittins policy that can
handle any combination of (a) multiple servers, (b) non-Poisson arrivals, and
(c) setup times. Our results thus cover the G/G/1 and G/G/k, with and without
setup times, bounding Gittins's suboptimality gap in each case. Each of (a),
(b), and (c) adds a term to our bound, but all the terms are negligible in
heavy traffic, thus implying Gittins's heavy-traffic optimality in all the
systems we consider. Another consequence of our results is that Gittins is
optimal in the M/G/1 with setup times at all loads.Comment: 41 page