Preemptive Resume Priority Call Center Model with Two Classes of MAP Arrivals

Generally in call centers, voice calls (say Type 1 calls) are given higher priority over e-mails (say Type 2 calls). An arriving Type 1 call has a preemptive priority over a Type 2 call in service, if any, and the preempted Type 2 call enters into a retrial buffer (of finite capacity). Any arriving call not able to get into service immediately will enter into the pool of repeated calls provided the buffer is not full; otherwise, the call is considered lost. The calls in the retrial pool are treated alike (like Type 1) and compete for service after a random amount of time, and can preempt a Type 2 call in service. We assume that the two types of calls arrive according to a Markovian arrival process (MAP) and the services are offered with preemptive priority rule. Under the assumption that the service times are exponentially distributed with possibly different rates, we analyze the model using matrix-analytic methods. Illustrative numerical examples to bring out the qualitative aspects of the model under study are presented

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

Linear retrial inventory system with second optional service under mixed priority service

The present paper deals with a generalization of the homogeneous single server finite source retrial inventory system with two classes of customers - one with high priority customer and the other with low priority customer. The inventory is replenished according to an (s, Q) policy and the replenishing times are assumed to be exponentially distributed. The server provides two types of services - one with essential service and the other with a second optional service. The service times of the 1st (essential) and 2nd (optional) services are independent and exponentially distributed. The high priority customers have a mixed priority over the low priority customers. Retrial is introduced for low priority customers only. The joint probability distribution of the number of customers in the waiting hall, the number of customers in the orbit and the inventory level is obtained for the steady state case. Some important system performance measures in the steady state are derived and the long-run total expected cost rate is also derived.Publisher's Versio

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

A Geo[X]/G[X]/1 retrial queueing system with removal work and total renewal discipline

Artículo definitivo disponible a través del doi: 10.1016/j.amc.2017.02.032In this paper we consider a discrete-time retrial queueing system with batch arrivals of geometric type and general batch services. The arriving group of customers can decide to go directly to the server expelling out of the system the batch of customers that is currently being served, if any, or to join the orbit. After a successful retrial all the customers in the orbit get service simultaneously. An extensive analysis of the model is carried out, and using a generating functions approach some performance measures of the model, such as the first distribution’s moments of the number of customers in the orbit and in the system, are obtained. The generating functions of the sojourn time of a customer in the orbit and in the system are also given. Finally, in the section of conclusions and research results the main contributions of the paper are commented.Proyecto TIN15-70266-C2-P-

Analysis of the finite-source multiclass priority queue with an unreliable server and setup time

In this article, we study a queueing system serving multiple classes of customers. Each class has a finite-calling population. The customers are served according to the preemptive-resume priority policy. We assume general distributions for the service times. For each priority class, we derive the steady-state system size distributions at departure/arrival and arbitrary time epochs. We introduce the residual augmented process completion times conditioned on the number of customers in the system to obtain the system time distribution. We then extend the model by assuming that the server is subject to operation-independent failures upon which a repair process with random duration starts immediately. We also demonstrate how setup times, which may be required before resuming interrupted service or picking up a new customer, can be incorporated in the model

Mathematical Analysis of Queue with Phase Service: An Overview

We discuss various aspects of phase service queueing models. A large number of models have been developed in the area of queueing theory incorporating the concept of phase service. These phase service queueing models have been investigated for resolving the congestion problems of many day-to-day as well as industrial scenarios. In this survey paper, an attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations. The methodology used by several researchers for solving various phase service queueing models has also been described. We have classified the related literature based on modeling and methodological concepts. The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein the phase type services are prevalent

Performance Modeling of Finite-Source Cognitive Radio Networks

This paper deals with performance modeling aspects of radio frequency licensing. The utilization of mobile cellular networks can be increased by the idea of the cognitive radio. Licensed users (Primary Users - PUs) and normál users (Secondary Users - SUs) are considered. The main idea is, that the SUs are able to access to the available non-licensed radio frequencies. A finite-source retrial queueing model with two non independent frequency bands (considered as service units) is proposed for the performance evaluation of the system. A service unit with a priority queue and another service unit with an orbit are assigned to the PUs and SUs, respectively. The users are classified into two classes: the PUs have got a licensed frequency, while the SUs have got a frequency band, too but it suffers from the overloading. We assume that during the service of the non-overloaded band the PUs have preemptive priority over SUs. The involved inter-event times are supposed to be independent and exponentially distributed random variables. The novelty of this work lies in the fact that we consider the effect of retrial phenomenon of SUs in performance modeling of radio frequency licensing by using a finite-source queueing model which takes the unreliability of radio transmission into account for the first time. In the literature, most work studied the performance of cognitive radio networks under a mixed spectrum environment of licensed and unlicensed bands where the blocked SUs and the preempted SUs are forced to leave the system forever when there are no idle channels in the system. But in practical situation, the blocked SUs and the preempted SUs may do not leave the system forever and try to continue their services after random amount of time. By the help of an appropriate continuous time Markov chain using MOSEL (MOdeling Specification and Evaluation Language) tool several numerical examples are provided showing the effects of different input parameters on the main performance measures of the cognitive radio networks. Our primary focus is to determine an optimal number of SUs, where at the secondary band the gained utilization, that is when switching to the cognitive radio, has a maximum value