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

Two queues with alternating service and switching times

tlThis paper is concerned with a system of two queues, attended by a single server who alternately serves one customer of each queue (if not empty). The server experiences switching times in his transition from one queue to the other. It is shown that the joint stationary queue-Iength distribution, at the instants at which the server becomes available to a queue, can be determined via transformation to a Riemann boundary value problem. The latter problem can be completely solved for general service- and switching-time distributions. The stationary distributions of the waiting times at both queues, and of the cycle times of the server, are also derived. The results obtained, and in particular the extensive numerical data for moments of waiting times and cycle times, yield insight into the behavior of more general cyclic-service modeIs. Such modeIs are frequenUy used to analyse polling systems

Availability assessment methods and their application in practice

In this paper we compare availability assessment methods for continuous production systems in a design phase. Apart from discussing simulation and analytical techniques, we also consider computer tools and data sources. The comparison is based on a literature search, analytical considerations and on practical experience with the methods and the tools. Most progress in the last ten years seems to have been made on simulation programs and on databases, such as OREDA. This is somewhat disappointing, compared with the progress made in a related area

Sojourn times in the M/G/1M/G/1 queue with deterministic feedback

In this paper we consider an M/G/1 queueing model, in which each customer is fed back a fixed number of times. For the case of negative exponentially distributed service times at each visit, we determine the Laplace-Stieltjes transform of the joint distribution of the sojourn times of the consecutive visits. As a by-result, we obtain the (transform of the) total sojourn time distribution; it can be related to the sojourn time distribution in the M/D/l queue with processor sharing. For the case of generally distributed service times at each visit, a set of linear equations is derived, from which the mean sojourn times per visit can be calculated