Waiting times in a two-queue model with exhaustive and Bernoulli service

Network Analysis;operations research

Optimization of polling systems with Bernoulli schedules

Optimization;Polling Systems;Queueing Theory;operations research

The power-series algorithm applied to cyclic polling systems

Polling Systems;Queueing Theory;operations research

Cyclic polling systems: Limited service versus Bernoulli schedules

Network Analysis;Polling Systems;miscellaneous issues

A numerical approach to cyclic-service queueing models

Queueing Theory;operations research

Stochastic decomposition in discrete-time queues with generalized vacations and applications

For several specific queueing models with a vacation policy, the stationary system occupancy at the beginning of a rantdom slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. For models in continuous time with Poissonian arrivals, this result is well-known, and referred to as stochastic decomposition, with proof provided by Fuhrmann and Cooper. For models in discrete time, this result received less attention, with no proof available to date. In this paper, we first establish a proof of the decomposition result in discrete time. When compared to the proof in continuous time, conditions for the proof in discrete time are somewhat more general. Second, we explore four different examples: non-preemptive proirity systems, slot-bound priority systems, polling systems, and fiber delay line (FDL) buffer systems. The first two examples are known results from literature that are given here as an illustration. The third is a new example, and the last one (FDL buffer systems) shows new results. It is shown that in some cases the queueing analysis can be considerably simplified using this property