510 research outputs found
Queue-length balance equations in multiclass multiserver queues and their generalizations
A classical result for the steady-state queue-length distribution of
single-class queueing systems is the following: the distribution of the queue
length just before an arrival epoch equals the distribution of the queue length
just after a departure epoch. The constraint for this result to be valid is
that arrivals, and also service completions, with probability one occur
individually, i.e., not in batches. We show that it is easy to write down
somewhat similar balance equations for {\em multidimensional} queue-length
processes for a quite general network of multiclass multiserver queues. We
formally derive those balance equations under a general framework. They are
called distributional relationships, and are obtained for any external arrival
process and state dependent routing as long as certain stationarity conditions
are satisfied and external arrivals and service completions do not
simultaneously occur. We demonstrate the use of these balance equations, in
combination with PASTA, by (i) providing very simple derivations of some known
results for polling systems, and (ii) obtaining new results for some queueing
systems with priorities. We also extend the distributional relationships for a
non-stationary framework
Workloads and waiting times in single-server systems with multiple customer classes
One of the most fundamental properties that single-server multi-class service systems may possess is the property of work conservation. Under certain restrictions, the work conservation property gives rise to a conservation law for mean waiting times, i.e., a linear relation between the mean waiting times of the various classes of customers. This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present. For a large class of such systems with interruptions, a decomposition of the amount of work into two independent components is obtained; one of these components is the amount of work in the corresponding systemwithout interruptions. The work decomposition gives rise to a (pseudo)conservation law for mean waiting times, just as work conservation did for the system without interruptions
Waiting times in discrete-time cyclic-service systems
Single-served, multiqueue systems with cyclic service in discrete time are considered. Nonzero switchover times between consecutive queues are assumed; the service strategies at the various queues may differ. A decomposition for the amount of work in such systems is obtained, leading to an exact expression for a weighted sum of the mean waiting times at the various queues
Analysis of a queuing model for slotted ring networks
We study a multi-server multi-queue system which is intended to model a local area network with slotted ring protocol. Two special cases of the model are analysed and the results are used to motivate an approach to approximate mean queue lengths in the general model
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