M/M/ Queue with ON-OFF Service Speeds

In this paper we analyze of a special kind of M/M/∞ queueing system. We assume that the rate of the servers alternates between two speeds according to an ON–OFF process whose ON periods are exponentially distributed and with general OFF periods. We look at the particular case where the OFF service rate is zero while the distribution of the OFF periods is heavy tailed, and for this case we derive the tail of the number of customers in the system. This model be applied to transportation systems where the M/M/∞ represents a delay line, such as a highway, whose crossing time may be unexpectedly interrupted for a long time by some accident.