Approximate expected delay costs for call and contact centre models under light traffic regimes

This paper studies the form of certain expected delay costs as a function of the arrival rate for customers who pass through a service facility that allows for reneging and retrials. We show that, under certain light traffic conditions, these costs are continuously increasing and convex functions of the arrival rate (within a finite interval). This result is first explored for the processor sharing system, in which a penalty cost is incurred for reneging from the service facility for good without ever receiving service, and then we consider a system with a more general structure governing the output processes and costs incurred per unit time, but without the penalty cost. A suggested application for these results, in which game theoretic considerations are utilized for gauging customer behaviour within a decentralized context, is briefly discussed

Essays on Service Information, Retrials and Global Supply Chain Sourcing

In many service settings, customers have to join the queue without being fully aware of the parameters of the service provider (for e.g., customers at check-out counters may not know the true service rate prior to joining). In such blind queues\u27\u27, customers typically make their decisions based on the limited information about the service provider\u27s operational parameters from past experiences, reviews, etc. In the first essay, we analyze a firm serving customers who make decisions under arbitrary beliefs about the service parameters. We show, while revealing the service information to customers improves revenues under certain customer beliefs, it may however destroy consumer welfare or social welfare. When consumers can self-organize the timing of service visits, they may avoid long queues and choose to retry later. In the second essay, we study an observable queue in which consumers make rational join, balk and (costly) retry decisions. Retrial attempts could be costly due to factors such as transportation costs, retrial hassle and visit fees. We characterize the equilibrium under such retrial behavior, and study its welfare effects. With the additional option to retry, consumer welfare could worsen compared to the welfare in a system without retrials. Surprisingly, self-interested consumers retry too little (in equilibrium compared to the socially optimal policy) when the retrial cost is low, and retry too much when the retrial cost is high. We also explore the impact of myopic consumers who may not have the flexibility to retry. In the third essay, we propose a comprehensive model framework for global sourcing location decision process. For decades, off-shoring of manufacturing to China and other low-cost countries was a no-brainer decision for many U.S. companies. In recent years, however, this trend is being challenged by some companies to re-shore manufacturing back to the U.S., or to near-shore manufacturing to Mexico. Our model framework incorporates perspectives over the entire life cycle of a product, i.e., product design, manufacturing and delivering, and after-sale service support, and we use it to test the validity of various competing theories on global sourcing. We also provide numerical examples to support our findings from the model

A survey of the machine interference problem

This paper surveys the research published on the machine interference problem since the 1985 review by Stecke & Aronson. After introducing the basic model, we discuss the literature along several dimensions. We then note how research has evolved since the 1985 review, including a trend towards the modelling of stochastic (rather than deterministic) systems and the corresponding use of more advanced queuing methods for analysis. We conclude with some suggestions for areas holding particular promise for future studies.Natural Sciences and Engineering Research Council (NSERC) Discovery Grant 238294-200

On the M/M/c/N Call Center Queue Modeling and Analysis

The M/M/c/c model is the most widely applied queueing model in the mathematical analysis of call centers. The M/M/c/c model is also referred to as the Erlang Loss System. The Erlang loss model does not take into consideration system attributes such as blocking and busy signals, balking and reneging, retrials and returns. Although, the Erlang loss model is analytically tractable, it is not easy to obtain insight from its results. The need to develop a more accurate call center model has necessitated the modification of the Erlang loss model. In this research, we model and analyze a call center using M/M/c/N the model. The goal of this paper is to extend existing results and prove new results with regards to the monotonicity and limiting behaviour of the M/M/c/N model with respect to the system capacity N

Transient Analysis of M[X1];M[X2]=G1;G2=1 Queueing Model with Retrial Priority Service, Negative Arrival, Two kinds of Vacations, Breakdown, Delayed Repair, Balking, Reneging and Feedback

This paper deals with the analysis of batch arrival retrial queue with two classes non-preemptive priorityunits, negative arrival, balking as well as reneging, feedback, emergency and Bernoulli vacation for anunreliable server. Here we assume that customers arrive according to compound Poisson process inwhich priority customers are assigned to class one and class two customers are of a low-priority type.If the server is free at the time of any batch arrivals, the customers of this batch begins to be servedimmediately. The low-priority customer may join the orbit with feedback if the service is not satisfied(or) may leave the system if the service is satisfied. The priority customers that find the server busyare queued and then served in accordance with FCFS discipline. The priority customers may renegethe queue if the server is not avilable in the system and there is no optional for feedback service tothe priority customers. The arriving low-priority customers on finding the server busy then they arequeued in the orbit in accordance with FCFS retrial policy without balking (or) may balk the orbit.While the server is serving to the customers, it faces two types of break-down there are breakdowns bythe arrival of negative customer and break-down at any instant of service and server will be down for ashort interval of time. Further concept of the delay time of repair is also introduced for breakdowns. Weconsider two different kinds of vacations, one is an emergency and the other one is Bernoulli vacation, theemergency vacation means at the time of the server serving the customer suddenly go for a vacation andthe interrupted customer waits to get the remaining service and after the completion of each service, theserver either goes for a vacation or may continue to serve for the next customer; if any . The retrial time,service time, vacation time, delay time and repair time are all follows general(arbitrary) distribution.Finally, we obtain some important performance measures of this model.Keywords:Batch arrival, priority queue, retrial queue, negative arrival, emergency and Bernoulli vacation, unreliableserver, breakdown and repair.AMSC: 60K25; 60K30; 90B2

On the M/M/c/N Call Center Queue Modeling and Analysis

The M/M/c/c model is the most widely applied queueing model in the mathematical analysis of call centers. The M/M/c/c model is also referred to as the Erlang Loss System. The Erlang loss model does not take into consideration system attributes such as blocking and busy signals, balking and reneging, retrials and returns. Although, the Erlang loss model is analytically tractable, it is not easy to obtain insight from its results. The need to develop a more accurate call center model has necessitated the modification of the Erlang loss model. In this research, we model and analyze a call center using M/M/c/N the model. The goal of this paper is to extend existing results and prove new results with regards to the monotonicity and limiting behaviour of the M/M/c/N model with respect to the system capacity N

The influence of information time in the strategic customer behavior

Σε πολλές εφαρμογές οι πελάτες φθάνουν σε ένα σύστημα αναμονής και αποφασίζουν αν θα μπουν σε αυτό η όχι χωρίς να γνωρίζουν το πλήθος των πελατών στο σύστημα. Αργότερα όμως, οι εισερχόμενοι πελάτες ενημερώνονται σχετικά με τον υπολειπόμενο χρόνο αναμονής τους στο σύστημα και τότε μπορούν να αποφασίσουν αν τους συμφέρει να παραμείνουν στο σύστημα ή όχι. Το βασικό ερώτημα που προκύπτει από την παραπάνω περιγραφή είναι κατά πόσο αυτή η καθυστερημένη πληροφορία επηρεάζει τη στρατηγική συμπεριφορά των πελατών. Στο πρώτο μέρος της διπλωματικής εργασίας παρουσιάζουμε τη βασική θεωρία της στρατηγικής συμπεριφοράς των πελατών σε Ουρές Αναμονής. Στο δεύτερο μέρος, παρουσιάζουμε δυο εργασίες με δομή καθυστερημένης πληροφορίας και με ποιο τρόπο αυτή επηρεάζει τη στρατηγική συμπεριφορά των πελατών. Στο τρίτο μέρος της εργασίας παρουσιάζομαι ένα πρωτότυπο μοντέλο με δομή καθυστερημένης πληροφορίας και προσπαθούμε να εξετάσουμε πως επηρεάζεται η στρατηγική συμπεριφορά των πελατών.In many applications customers arrive in a service system and decide whether to join it or not, without knowing the number of customers in the system. Later, the joining customers get informed about their position in the system and then they can decide wheter to stay in it or balk. The main question that arises from this description, is in what way this delayed information influence strategic customer behavior. In the first part of this MSc Thesis we present the main theory of Strategic Customers in Queueing Systems. In the second part, we present two papers with a dealyed information structure. In the third part, we present a new model with a delayed information structure and we try to analyze in what way this dealyed information influence strategic customer behavior

Equilibrium and Optimal Strategies in M/M/1 Queues with Working Vacations and Vacation Interruptions

We consider the customers equilibrium and socially optimal joining-balking behavior in single-server Markovian queues with multiple working vacations and vacation interruptions. Arriving customers decide whether to join the system or balk, based on a linear reward-cost structure that incorporates their desire for service, as well as their unwillingness for waiting. We consider that the system states are observable, partially observable, and unobservable, respectively. For these cases, we first analyze the stationary behavior of the system and get the equilibrium strategies of the customers and compare them to socially optimal balking strategies numerically