Hirotaka Sakasegawa

On the equivalence of three types of blocking in non-Markovian tandem queues

Definitions of blocking types for tandem queueing systems are given where each stage consists of multiple servers. Some of them are shown to be identical with respect to service initiation epochs at each stage. Such identical relationships are proved using sample path correspondence, and are therefore valid irrespective of the arrival process and the service time distributions.

Some Properties of Throughput in a Queueing Network with Changing-Speed Servers and Blocking

A class of queueing networks, called the Jackson networks, is well known to have a convenient property for queue length distributions, namely, the so-called product form (see, e.g.,Walrand [5]). This property enables us to calculate the queue length distributions for large-scale queueing networks, and hence Jackson networks have been used extensively in the design or performance evaluation of communication systems. On the other hand, these queueing networks have not been used so often for manufacturing systems. Of course, there are exceptions, e.g., an attempt has been made to apply the networks to flexible manufacturing systems (FMSs; for details, see [1]). Why haven’t these networks been used so often for manufacturing systems? We think there are two main reasons. One is the structure of Jackson networks. Each node (or station) in a manufacturing system usually has only a finite buffer capacity, so a blocking phenomenon may occur. In this case, it is very important to evaluate how the performance parameters such as the production rate (throughput) are affected by blocking. In Jackson networks, however, there is no blocking. The other reason is the service time distribution of jobs at each station. In Jackson networks, this distribution is exponential—an unacceptable situation for practitioners working on manufacturing systems. Of course, there are exceptions in this context, e.g., symmetric queueing networks by Kelly [2]. For these reasons, tandem queues with blocking and general service time distribution at each station have been used in the design or performance evaluation of manufacturing systems such as flow lines, transfer lines, and flexible assembly lines (see, e.g., [7] and [1]).

Note on throughput in a queueing network with changing-speed servers and blocking

We consider a queueing network under very general settings. The network is related to tandem queues with blocking rather than queueing networks with product-form queue length distributions or insensitivity. Our queueing network in which each station has only finite buffer capacity and in which the processing (service) capacity as a whole depends on the total busy servers is of interest to practitioners working on the design or control of manufacturing systems and related systems. We focus on the throughput of the network. The main purpose of this paper is not to analyze the throughput but to present its properties which give a good insight into the problem. We derive two expressions of the throughput in terms of the corresponding regular queueing network. Based on the first expression, we show that a two-station tandem queue with changing-speed servers is reversible with respect to the throughput. A sensitivity analysis is given as an application of the second expression.