Transient behaviour of a double-channel Markovian queue with limited waiting space (Q1110203)

In this paper, a two-server queue with a finite capacity and exponential arrival and service distributions is considered (i.e. an M/M/2/N queue). The interarrival and service times have exponential distributions with parameters \(\lambda\) and \(\mu\), respectively. Service time has the same distribution for both servers. Explicit formulae for \(p_ n(t)\)- the probabilities that at time t there are n customers in the system - are derived. A formula for mean queue length at time t is also given. The paper also contains tables presenting numerical values of \(p_ n(t)\) for the case when the queue capacity \(N=9\) and for various \(\lambda\), \(\mu\) and t.