A study of a bulk unreliable Markovian network (Q1968535)

The model considered in this paper comprises \(N\) stations (concentrators) with customers arriving in Poisson streams to each station. Customers are served by `buses' (mobile multichannel servers) which arrive in a Poisson stream and traverse the stations in the order 1 to \(N\) picking up customers as they go. Each bus has a finite capacity and performs its tasks, of loading customers and travelling between stations, instantaneously. An added complexity is that buses can break down according to station-dependent probabilities, at which point they unload all their customers, leaving them at the station for future buses to pick up. A customer's service is completed when it has been carried past station \(N\). The authors perform a station by station analysis, beginning with station 1, to evaluate the probability generating function of the number of customers, and the throughput, at each station.