Waiting times for the CPB system (Q1312676)

The authors investigate a nonsymmetric cyclic priority batch system under the following assumptions: (1) there are \(N\) stations and \(k\) queues at each station; (2) a single server is moving along the cycle servicing the customers at each station; (3) arrivals at each station and at each queue are of Poisson type with given parameter, the service time distribution is general; (4) the priority of a queue is determined on the basis of the number of customers presently in it. The authors concentrate their attention on the determination of state probabilities at moments when the server starts and finishes its work at a queue during equilibrium. On the basis of obtained generating functions some further characteristics of service are computed. A numerical example illustrates the described method.