Conditions for stability and instability of retrial queueing systems with general retrial times

We study the stability of single server retrial queues under general distribution for retrial times and stationary ergodic service times, for three main retrial policies studied in the literature: classical linear, constant and control policies. The approach used is the renovating events approach to obtain sufficient stability conditions by strong coupling convergence of the process modeling the dynamics of the system to a unique stationary ergodic regime. We also obtain instability conditions by convergence in distribution to improper limiting sequences

Standard and retrial queueing systems: a comparative analysis

We describe main models and results of a new branch of the queueing theory, theory of retrial queues, which is characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.)leaves the service area, but after some random delay returns to the system again. Emphasis is done on comparison with standard queues with waiting line and queues with losses. We give a survey of main results for both single server M/G/1 type and multiserver M/M/c type retrial queues and discuss similarities and differences between the retrial queues and their standard counterparts. We demonstrate that although retrial queues are closely connected with these standard queueing models they, however, ossess unique distinguished features. We also mention some open problems.We describe main models and results of a new branch of the queueing theory, theory of retrial queues, which is characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.)leaves the service area, but after some random delay returns to the system again. Emphasis is done on comparison with standard queues with waiting line and queues with losses. We give a survey of main results for both single server M/G/1 type and multiserver M/M/c type retrial queues and discuss similarities and differences between the retrial queues and their standard counterparts. We demonstrate that although retrial queues are closely connected with these standard queueing models they, however, ossess unique distinguished features. We also mention some open problems

Diffusion limit for single-server retrial queues with renewal input and outgoing calls

This paper studies a single-server retrial queue with two types of calls (incoming and outgoing calls). Incoming calls arrive at the server according to a renewal process, and outgoing calls of N − 1 (N ≥ 2) categories occur according to N − 1 independent Poisson processes. Upon arrival, if the server is occupied, an incoming call joins a virtual infinite queue called the orbit, and after an exponentially distributed time in orbit enters the server again, while outgoing calls are lost if the server is busy at the time of their arrivals. Although M/G/1 retrial queues and their variants are extensively studied in the literature, the GI/M/1 retrial queues are less studied due to their complexity. This paper aims to obtain a diffusion limit for the number of calls in orbit when the retrial rate is extremely low. Based on the diffusion limit, we built an approximation to the distribution of the number of calls in orbit

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 Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia

The impact of disruption characteristics on the performance of a server

In this paper, we study a queueing system serving N customers with an unreliable server subject to disruptions even when idle. Times between server interruptions, service times, and times between customer arrivals are assumed to follow exponential distributions. The main contribution of the paper is to use general distributions for the length of server interruption periods/down times. Our numerical analysis reveals the importance of incorporating the down time distribution into the model, since their impact on customer service levels could be counterintuitive. For instance, while higher down time variability increases the mean queue length, for other service levels, can prove to be improving system performance. We also show how the process completion time approach from the literature can be extended to analyze the queueing system if the unreliable server fails only when it is serving a customer