Rejection rules in the \(M/G/1\) queue
It is considered the \(M/G/1\) queue with impatient customers. The following basic cases are investigated: 1) the waiting time is restricted by a random barricade (r.b.), 2) the sojourn time (waiting time plus service time) does not exceed a r.b., and service time may be reduced if necessary, 3) a customer is totally lost if sojourn time exceeds a r.b. It is assumed that the workload upon arrival is known either to the server or to the arriving customer in the cases 1) and 3). The paper gives new results and some review material. Both steady-state distribution (as the solution of Volterra equation) and busy period analysis (including martingale one) are considered. The authors concentrate on the exponential service times and deterministic or exponential barricade. In the last case a birth-death process is used to find an explicit solution for busy period Laplace transformation.
scientific article; zbMATH DE number 765312
scientific article