A multiserver retrial queue: regenerative stability analysis

Abstract

ARTICLE INFO ABSTRACT In this paper, we study the stationary analysis of the model M/M/3/n+1 with linear retrial rates and with state dependent parameters by introducing the bivariate process {(C(t), Q(t)), t  0}. Some numerical results are also presented.

Stability analysis of multiserver discrete-time queueing systems with renewal-type server interruptions

“…In this case the rate of the actual interruptions approaches the rate of the blocked periods because the queue is almost always busy. This effect has been observed in many other models, see for instance [34]. Nevertheless, the estimate of the capacity loss by the service repetitions can be further refined as shown in Section 6.2.…”

“…The key step of the stability analysis presented below is to establish that β(t) ⇒ ∞ (in probability) which implies α 0 < ∞. Such an approach has been successfully applied before, see amongst others [34,38].…”

“…By (34) we can then realise a cycle of length k 0 j 0 during which at least k 0 + 1 customers are served and k 0 interarrival times of length j 0 are realised with positive probability. We can thus reduce the queue size while retaining synchronisation between T and A.…”

“…For preemptive repeat disciplines one intuitively sees that some service capacity is lost whenever service is interrupted. This contribution is the first to tackle the problem of the stability of queues with service interruptions with a regenerative stochastic process approach [33,34], enabling us to prove the obtained conditions rigorously. The main contribution of the current work is its generality.…”

Stability of Constant Retrial Rate Systems with NBU Input*

“…Note that if μ 0 increases, then the stability region delimited by condition (8) approaches the actual stability region, delimited by requirement (4). It can be deduced from [15] that as μ 0 increases, the original retrial system approaches the classical system with an infinite buffer, for which the stability criterion is ρ := λ/μ < 1. This explains why the curve μ L (μ 0 ) depicted on Fig.…”