Stability Analysis and Simulation of N-Class Retrial System With Constant Retrial Rates and Poisson Inputs

Abstract

In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate µ (i) 0 ) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) * Corresponding author

Optimal and Equilibrium Retrial Rates in Single-Server Multi-orbit Retrial Systems

“…Remark 1. The equivalence of both systems from the point of view of class-1 customers follows from discussion in the work [6] where more detailed analysis of unstable orbits can be found.…”

“…Thus, the analysis of original K-orbit system with arbitrary K is reduced to the analysis of the auxiliary systemΣ. Note that the stability conditions found in [6,5] allow to select the corresponding parameters in such a way that the 1st class orbits in both systems are always stable, while the 2nd class orbit in system Σ may be either stable or unstable. Now we focus on two-orbit system Σ and recall that the 1-class orbit in the system Σ is assumed to be stable.…”

“…Thus, our approximation can be interpreted as equilibrium rate in game theoretic framework. It follows from [5,6] that the necessary stability conditions of original system are…”

On the ergodicity bounds for a constant retrial rate queueing model

“…A sufficient stability condition of the general single-class retrial system with constant retrial rate described above is obtained in [5]. Stability analysis of multi-class retrial system is presented in [6].…”

Sufficient stability conditions for multi-class constant retrial rate systems

“…Then, in [18] the model of [26] was extended to associate different phases of service with different retrial classes. In [7] necessary stability conditions were obtained for the case of a single-server, multi-class retrial queue with constant retrial rates. Recently in [9] the authors studied the two-class Markovian retrial queueing system with one server, no buffer and with constant retrial rates.…”