Probing a M/G/1 queue with general input and service times

Abstract

We consider the estimation of the arrival rate and the service time moments of a $M/G/1$ queue with probing, i.e., with special customers (probes) entering the system. The probe inter-arrival times are i.i.d. and probe service times follow a general positive distribution. The only observations used are the arrival times, service times and departure times of probes. We derive the main equations from which the quantities of interest can be estimated. Two particular probe arrivals, deterministic and Poisson, are investigated.