On single-server closed queues with priorities and state dependent parameters
The author considers two interrelated queueing models with finite customer population and obtains the limiting probabilities of these systems by employing the techniques of semi-regenerative processes. The first model deals with m working machines and \((w+1)\) reserve machines, each one of which replaces any working machine that breaks down. These machines (customers) on break down are served by a single repairman (server). The word ``priority'' pertains to the two types of machines (which are inactuality indistinguishable) and not to the service discipline of the system. The mean arrival rate and repair time distributions are assumed to depend on the total number of machines in good condition. The repair man will remain idle during the period when all the machines are intact. The second model is almost the same as the first, except that in this case there are w reserve machines and as soon as all the \((m+w)\) machines are intact, the repairman takes a vacation for a random duration and arrives with a new machine which replaces either one of the defective machines, if any or a reserve machine in case of no failures. A special case of this model is shown to reduce to an equivalent GI/M/m/w system. A connection between the two models is established. Some special cases and examples are also discussed.
queueing models with finite customer population
scientific article; zbMATH DE number 4211234