A queueing system with K servers operates in the following manner. When the system is empty, arriving customers are attended by only one server. A set of forward threshold values is defined so that at epochs at which the number of customers in the system exceeds a forward threshold value an extra server is added. Similarly, a set of reverse threshold values is defined so that at epochs at which the number of customers in the system becomes less than a reverse threshold value one server is removed. The forward and reverse threshold values are assumed to be different. Closed-form occupancy distribution and mean delay of customers in the system are obtained by the Green's function method.

A mobile cellular communication system is considered. The calls arriving at the base station of each cell are modeled by a queueing system with two arrival streams. Stream 1 (also called class 1) arrivals are those calls in progress that are handed over to the cell from other cells, and class a arrivals are those calls that are originating in the cell. The guard channel scheme is considered in which arriving calls are indiscriminately assigned channels within a cell as long as the number of busy channels in the cell is below a predefined threshold. When this number reaches the threshold, only arriving class 1 calls are assigned channels immediately; arriving class 2 calls are queued. When all the channels are busy, then arriving class 1 calls are lost while class 2 calls continue to be queued. The system is analysed by a generating function method which utilizes the structure of the model to give a very concise solution.>

A client-server system is a distributed system where a server station receives requests from its client stations, processes the requests and returns replies to the requesting stations. The authors consider client-server systems in which a set of workstations access a file server over a local area network. The systems are modelled by a class of stochastic Petri nets. The mean response time, the throughput and the parametric sensitivities are evaluated for a client-server system based on token ring network and a system based on CSMA/CD network. These models are different from the prevalent performance models of token ring or CSMA/CD network systems because of the message interdependencies introduced by the clients-server structure. An approximate analytic-numeric method rather than simulation is used to solve the models. The solution method and the accuracy of approximation are also discussed.>

The reliability of extra-stage interconnection networks is discussed. Three types of reliability are analyzed: terminal reliability, which is the probability that at least one fault-free path exists between a given input-output pair: network reliability, which is the probability that at least one fault-free path exists between every input-output pair; and broadcast reliability, which is the probability that at least one fault-free path exists between a given input and all outputs. A recursive expression for the broadcast reliability is obtained. Tight bounds are derived for the network reliability. The numerical results indicate that for practical networks (i.e. when network reliability is at least 0.5) the difference between the upper bound and the lower bound is no more than 2% of the lower bound.>

Finite population and finite capacity polling systems are considered. The behavior of these systems is described by means of generalized stochastic Petri nets. The exact results for the mean response times are obtained numerically by means of a stochastic Petri net package. Finite population polling systems are generally difficult to analyze. The results obtained can be used to validate approximate solutions to the above class of polling systems when such solutions become available.>

Various methods for interconnecting local area networks (LANs) are studied, both direct interconnection schemes, and backbone network interconnection schemes. The latter can be either broadcast networks (bus or ring) or switched networks. For a ring-based broadcast backbone network interconnections scheme, the authors assume that the counter-rotating ring is used. For the direct interconnection scheme, they assume that eight LANs are so connected that the underlying topology is a hypercube. For the switched-backbone network interconnection scheme, they assume that the topology of the backbone network is the hypercube. The reliability and availability of the different schemes are analyzed. Numerical results indicate that under the set of assumptions made, the direct interconnection scheme has the highest reliability and availability, followed by the bus-based interconnection scheme, the ring-based interconnection scheme, and the switched backbone interconnection scheme, in that order.>

Consideration is given to token-passing or polling systems in which the message arrival process, the message transmission time distribution, and the walk time vary from one station to another. An approximate analysis of these systems is obtained. The results obtained from the approximate analysis are compared against both simulation results and those obtained from two approximate methods that have been proposed earlier. For the special case of a symmetric system, it is shown that the approximate analysis is exact when the walk time is constant. Even when the walk time is exponentially distributed, it is shown that the approximate analysis gives an approximation error of less than 0.3% in the range of offered load that is generally of interest.>