Queue lengths and workloads in polling systems

Details Queue lengths and workloads in polling systems Queue lengths and workloads in polling systems

2011-06-06

arxiv.org/abs/1106.0964v2

Operations Research Letters 39 (2011) 401-405

Mathematics

Probability

Scientific paper

10.1016/j.orl.2011.10.006

We consider a polling system: a queueing system of $N\ge 1$ queues with Poisson arrivals $Q_1,...,Q_N$ visited in a cyclic order (with or without switchover times) by a single server. For this system we derive the probability generating function $\mathscr Q(\cdot)$ of the joint queue length distribution at an arbitrary epoch in a stationary cycle, under no assumptions on service disciplines. We also derive the Laplace-Stieltjes transform $\mathscr W(\cdot)$ of the joint workload distribution at an arbitrary epoch. We express $\mathscr Q$ and $\mathscr W$ in the probability generating functions of the joint queue length distribution at visit beginnings, ${\mathscr V}_{b_i}(\cdot)$, and visit completions, ${\mathscr V}_{c_i}(\cdot)$, at $Q_i$, $i=1,...,N$. It is well known that ${\mathscr V}_{b_i}$ and ${\mathscr V}_{c_i}$ can be computed in a broad variety of cases. Furthermore, we establish a workload decomposition result.

Affiliated with

Also associated with

No associations

Rating

Queue lengths and workloads in polling systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Queue lengths and workloads in polling systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Queue lengths and workloads in polling systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-389059