Analysis of GI^X/M(n)//N systems with stochastic customer acceptance policy

Queueing Systems, 58(1) (2008), 29-55
http://dx.doi.org/10.1007/s11134-007-9057-2

We investigate GI X /M(n)//N systems with stochastic customer acceptance policy, function of the customer batch size and the number of customers in the system at its arrival. We address the time-dependent and long-run analysis of the number of customers in the system at prearrivals and postarrivals of batches and seen by customers at their arrival to the system, as well as customer blocking probabilities. These results are then used to derive the continuous-time long-run distribution of the number of customers in the system. Our analysis combines Markov chain embedding with uniformization and uses stochastic ordering as a way to bound the errors of the computed performance measures.