Abstract

This paper presents a multinomial model for a special case of the machine interference problem (MIP), where each of N identical machines randomly requests several different service types. The model allows the calculation of the expected interference time in the queue for each service type. The extended version of the model allows calculation of the exact distribution function of the steady state waiting time and total service time for each type of requested service. In addition, the model can be adjusted for the case where the service is provided by a group of K identical operators, each operator is capable to handle all types of service, but each service type has a different priority.