Calculation of the steady state waiting time distribution in the context of the machine interference problem

This paper proposes an extension of a multinomial model for the machine interference problem, where each of N identical machines randomly requests several different service types. Each request for a service is fulfilled by an operator who can provide only one type of service. The extended model is useful for the case in which there is a time limit for one service type (or more), such that it must be accomplished within a certain time from the moment of the request. A delay in the service above a given time spoils the product and makes it useless for its intended purpose. The model allows calculation of the exact distribution function of the steady state waiting time and total service time (waiting time + service time) for each type of requested service, for the first come first served (FCFS) queue discipline.