Retrial queueing models in discrete time: a short survey of some late arrival models

Abstract

This paper presents an overview of one-server queueing models with retrials in discrete-time. In all these models the number of primary customers arriving in a time slot follows a general probability distribution and the different numbers of primary arrivals in consecutive time slots are mutually independent. Each customer requires from the server a generally distributed number of slots for his service, and the service times of the different customers are independent. Only models with delayed access are considered, and the socalled late arrival setup is chosen. For all the models the steady-state behavior is studied through the generating function of the number of customers in the orbit. From the generating function several performance measures are deduced, like the average orbit size and the mean busy period.

Waiting Time Asymptotic Analysis of a M/M/1 Retrial Queueing System Under Two Types of Limiting Condition

“…This equation is equal to the coefficient of the derivative ∂g(x,u) ∂x . Then the coefficient is zero in (24) and k = x:…”

“…Main fields where such models are used are telecommunication networks, computer networks, call centers, wireless communication systems, cognitive networks, cloud computing. An extensive review of recent developments and methods related to RQ systems one can find in, for example, Artalejo, Falin [2], Artalejo, Gomez-Corral [3], Gomez-Corral, Phung-Duc [16], Falin, Templeton [13], Kim, Kim [17], Nobel [24], Phung-Duc [26].…”

Performance analysis of polling‐based MAC protocol with retrial for Internet of Things

“…Altman and Yechiali 18 study a closed polling model in which all customers finished service at a queue would proceed to another (possibly the same) queue but not leave. Several one‐server queue models with retrial are present 19–21 . However, this paper did not consider a polling setting.…”

“…Several one-server queue models with retrial are present. [19][20][21] However, this paper did not consider a polling setting. Sidi and Levy 22 consider a system in which (external) customers arrive at a queue according to a Poisson process and in which a customer, after having received service at a queue, either leaves the system or moves to another queue (with some given probability).…”

“…Assume the system is symmetric. Solving the simultaneous equations j, k) with (18) and (19) and j, j) with (20) and (21), we can get the second moment of the generating function as shown in (22)…”