The M/G/1/∞ System in the Nested Markov Chain Method in Mechanical Engineering

Abstract

The M/G/1/∞ system is a non-Markov model, a single-line queueing system with waiting and a Poisson incoming flow of demands of intensity λ. However, the letter G in the second place of the system entry means that the service time of each demand can be distributed according to an arbitrary law G(x). If G(x) is not hyper-Erlangian, then it is impossible to construct a process η(t) that would describe the functioning of the system and would be a Markov process with continuous time and a discrete set of states. In particular, the number of demands in the system ν(t) at time t will not be such a process, since the distribution of the remaining service time of a demand in the system, unlike the exponential case, depends on the time that this demand has already been serviced.