A comparison of the stationary distributions of GI/M/c/nand GI/M/c

In this note, we compare the arrivaland time stationary distributionsof the number of customers in the GI/M/c/nand GI/M/cqueueing systems as ntends to infinity. We show that earlier results established for GI/M/1/nand GI/M/1 remain true. Namely, it is proved that if the interarrival time c.d.f. His non lattice with mean value ?-1and if the traffic intensity is strictly less than one, then the convergence rates in l1normof the arrival and time stationary distributions of GI/M/c/nto the corresponding stationary distributions of GI/M/care geometric and are characterized by ?, the unique solution in (0,1) of the equation z= ?80exp{-µc(1-z)t}dH(t).