Asymptotic investigation of fully available switching systems with high repetition intensity of blocked calls (Q1062359)

An M/M/c/0 loss system is considered where blocked calls (customers) retry to gain access to the system after an exponentially distributed period of mean \(\mu^{-1}\). The intuitively obvious result is proved that for \(\mu\) \(\to \infty\) the stationary distribution of having i calls in the system and j calls in the pool of blocked calls equals the stationary distribution of having i calls in service and j calls waiting in an ordinary M/M/c queue. Without explicit proofs some interesting and useful asymptotic results for the blocking probability and the mean number of calls in the pool of blocked calls are subsequently given.