Confidence Intervals Associated with Performance Analysis of Symmetric Large Closed Client/server Computer Networks

The paper studies a closed queueing network containing a server station and k identical client stations. The client stations are subject to breakdowns, and a lifetime of each client station is assumed to be a random variable independent of all other ones having the probability distribution ) (x G . The server station is an infinite server queueing system, and client stations are single server queueing systems with autonomous service, i.e. every client station serves customers (units) only at random instants generated by strictly stationary and ergodic sequence of random variables. The total number of units in the network is . N The service times of units in the server station are independent exponentially distributed with parameter . λ The expected times between departures in client stations are . ) ( 1 − μ N After a service completion in the server station a unit is transmitted to the j th client station with equal probability l / 1 , where k l ≤ is the number of currently available (i.e. not failure) client stations, and being processed in the j th client station the unit returns to server station. The parameter N is assumed to be large. The aim of this paper is to study the behaviour of bottleneck queues and to find confidence intervals associated with increasing a given high level of queue proportional to N in client stations.