Insensitivity in discrete time queues with a moving server
Two single-server queues in discrete time are considered. The customers have in general different types and request several service segments. The server can move from one customer to another after completion of each segment of service. In the first model one segment is provided at each time point while in the second model at most one arrival or service occurs at each point (in fact the second model is considered in so-called ``stomer time scale''). The states of the queue are described by the discrete time Markov (birth and death) process with a given transient probability. The conditions for the existence of limiting (product form) distributions are found. The conditions are obtained also when the distributions are insensitive to the service distribution and queue discipline. Some special cases, in particular, Daduna and Schassberger model are considered.
insensitive to the service distribution and queue discipline
scientific article; zbMATH DE number 98551