Stability Condition of a Retrial Queueing System with Abandoned and Feedback Customers

This paper deals with the stability of a retrial queueing system with two orbits, abandoned and feedback customers. Two independent Poisson streams of customers arrive to the system, and flow into a single-server service system. An arriving one of type i; i = 1; 2, is handled by the server if it is free; otherwise, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. The customer in the orbit either attempts service again after a random time or gives up receiving service and leaves the system after a random time. After the customer is served completely, the customer will decide either to join the retrial group again for another service or leave the system forever with some probability

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Stability condition of multiclass classical retrials: a revised regenerative proof

We consider a multiclass retrial system with classical retrials, and present a new short proof of the sufficient stability (positive recurrence) condition of the system. The proof is based on the analysis of the departures from the system and a balance equation between the arrived and departed work. Moreover, we apply the asymptotic results from the theory of renewal and regenerative processes. This analysis is then extended to the system with the outgoing calls. A few numerical examples illustrate theoretical analysis

A Note on an M/M/s Queueing System with two Reconnect and two Redial Orbits

A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new attempt to reach the primary queue, and when a customer finishes his conversation with a server, he may comeback to the system, to one of the reconnect orbits where he will wait for another service. In this paper, a fluid model is used to derive a first order approximation for the number of customers in the redial and reconnect orbits in the heavy traffic. The fluid limit of such a model is a unique solution to a system of three differential equations

A Multiclass Retrial System With Coupled Orbits And Service Interruptions: Verification of Stability Conditions

In this work, we investigate the stability conditions of a multiclass retrial system with coupled orbit queues and service interruptions. We consider a single server system accepting N classes of customers according to independent Poisson inputs and with class-dependent, arbitrarily distributed service times. An arriving customer who finds the server unavailable upon arrival, joins the corresponding orbit queue according to its class. We assume that the ?rst (oldest) blocked customer in an orbit queue attempts to connect with the server after an exponentially distributed service time, which depends both on its class, and on the current state (busy or idle) of the other orbit queues. During service times, interruptions occur according to class-dependent Poisson process, following by class-dependent arbitrarily distributed setup times. We consider both preemptive- repeat identical, and preemptive-resume interruptions. Potential applications of such a system can be found in the modelling of relay-assisted cooperative wireless networks. We focus on the non-symmetrical orbits and perform simulation experiments for the system with three classes of customers to verify stability conditions for both types of the server interruptions

Analysis of a Generalized Retrial System with Coupled Orbits

We study a single-server retrial queueing model with N classes of customers following independent Poisson inputs. A class-i customer, which meets server busy, joins a type-i orbit. Then orbital customers try to occupy the server using a modified constant retrial policy called coupled orbit queues policy. Namely, the orbit i retransmits a class-i customer to server after an exponentially distributed time with a rate which depends in general on the binary states (busy or not) of other orbits j /= i. The service times have general class-dependent distribution and the model is described by a non-Markov regenerative process. This model is motivated by increase the impact of wireless interference. We apply regenerative approach and local balance equations to obtain necessary stability conditions and some bounds on the important performance measures of the model. Moreover, we suggest also a sufficient stability condition and verify our results numerically by simulation experiments

Stability condition of multiclass classical retrials: a revised regenerative proof

We consider a multiclass retrial system with classical retrials, and present a new short proof of the sufficient stability (positive recurrence) condition of the system. The proof is based on the analysis of the departures from the system and a balance equation between the arrived and departed work. Moreover, we apply the asymptotic results from the theory of renewal and regenerative processes. This analysis is then extended to the system with the outgoing calls. A few numerical examples illustrate theoretical analysis

Steady-state analysis of a multiclass MAP/PH/c queue with acyclic PH retrials

A multiclass c-server retrial queueing system in which customers arrive according to a class-dependent Markovian arrival process (MAP) is considered. Service and retrial times follow class-dependent phase-type (PH) distributions with the further assumption that PH distributions of retrial times are acyclic. A necessary and sufficient condition for ergodicity is obtained from criteria based on drifts. The infinite state space of the model is truncated with an appropriately chosen Lyapunov function. The truncated model is described as a multidimensional Markov chain, and a Kronecker representation of its generator matrix is numerically analyzed. © Applied Probability Trust 2016