INSTANT-SERVICE QUEUING-NETWORKS - I - SINGLE-TYPE CUSTOMER MODEL

Two classes of queueing networks are investigated, in which customers either join the queue at a server with some probability or instantly j ockey with some additional probability to another server according to a routing matrix. Fbr the first class, the probability that a customer joins a particular server depends an the queue size at the server and number of the server from which he jockeyed (customers who arrive fro m outside are assigned a zero serial number), whereas for the second c lass it depends on the server state. The first class includes both ope n and closed networks, whereas the second class consists only of open networks. Ebr open networks, arrivals are assumed to be simple. The se rvice times at servers of the first class are exponentially distribute d, whereas at isolated servers of the second class they are quasiinver se Markov processes. The stationary distribution for both classes is m ultiplicative, and the arrivals Sor the second class are independent P oisson inputs.