DYNAMIC STAFFING IN A TELEPHONE CALL CENTER AIMING TO IMMEDIATELY ANSWER ALL CALLS

This paper proposes modeling and analysis methods to facilitate dynamic staffing in a telephone call center with the objective of immediately answering all calls. Because of this goal, it is natural to use infinite-server queueing models. These models are very useful because they are so tractable. A key to the dynamic staffing is exploiting detailed knowledge of system state in order to obtain good estimates of the mean and variance of the demand in the near future. The near-term staffing needs, e.g., for the next minute or the next twenty minutes, can often be predicted by exploiting information about recent demand and current calls in progress, as well as historical data. The remaining holding times of calls in progress can be predicted by classifying and keeping track of call types, by measuring holding-time distributions and by taking account of the elapsed holding times of calls in progress. The number of new calls in service can be predicted by exploiting information about both h..

Scaling limits for infinite-server systems in a random environment

This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate $\Lambda$ from a given distribution every $\Delta$ time units, yielding an i.i.d. sequence of arrival rates $\Lambda_1,\Lambda_2, \ldots$. Applying a martingale central limit theorem, we obtain a functional central limit theorem for the scaled queue length process. We proceed to large deviations and derive the logarithmic asymptotics of the queue length's tail probabilities. As it turns out, in a rapidly changing environment (i.e., $\Delta$ is small relative to $\Lambda$) the overdispersion of the arrival process hardly affects system behavior, whereas in a slowly changing random environment it is fundamentally different; this general finding applies to both the central limit and the large deviations regime. We extend our results to the setting where each arrival creates a job in multiple infinite-server queues

IS PREVENTION ALWAYS BETTER? A CASE OF IT SERVICE MANAGEMENT

Information Technology Infrastructure Library (ITIL), a framework for IT Service Management (ITSM), emphasizes the need for an ongoing preventive activity woven into the fabric of enterprise IT of organizations as opposed to a reacting to a specific situation. However, with the increasing focus on cost reduction, it is essential to revisit the trade-off between costs and other primary ITSM objectives such as service availability and quality. With this basic premise, we compare the cost of conducting IT service operations with varying levels of prevention. We modelled the IT service operation processes based on queuing and software reliability theories while assessing the impact of exogenous variables such as initial application maturity, drop rates & monitoring cost. We illustrated that optimum lies between the extremes of complete prevention and reaction. Also, we were able to observe the pronounced impact of staffing stickiness on the results

Rare-event analysis of mixed Poisson random variables, and applications in staffing

A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this paper we consider a mixed Poisson arrival process with arrival rates that are resampled every $N^{a}$ time units, where $a> 0$ and $N$ a scaling parameter. In the first part of the paper we analyse the asymptotic tail distribution of this doubly stochastic arrival process. That is, for large $N$ and i.i.d. arrival rates $X_1, \dots, X_N$, we focus on the evaluation of $P_N(A)$, the probability that the scaled number of arrivals exceeds $NA$. Relying on elementary techniques, we derive the exact asymptotics of $P_N(A)$: For $a 3$ we identify (in closed-form) a function $\tilde{P}_N(A)$ such that $P_N(A) / P_N(A)$ tends to $1$ as $N \to \infty$. For $a \in [\frac{1}{3},\frac{1}{2})$ and $a\in [2, 3)$ we find a partial solution in terms of an asymptotic lower bound. For the special case that the $X_i$s are gamma distributed, we establish the exact asymptotics across all $a> 0$. In addition, we set up an asymptotically efficient importance sampling procedure that produces reliable estimates at low computational cost. The second part of the paper considers an infinite-server queue assumed to be fed by such a mixed Poisson arrival process. Applying a scaling similar to the one in the definition of $P_N(A)$, we focus on the asymptotics of the probability that the number of clients in the system exceeds $NA$. The resulting approximations can be useful in the context of staffing. Our numerical experiments show that, astoundingly, the required staffing level can actually decrease when service times are more variable

Some asymptotic properties of the Erlang-C formula in many-server limiting regimes

This paper presents asymptotic properties of the Erlang-C formula in a spectrum of many-server limiting regimes. Specifically, we address an important gap in the literature regarding its limiting value in critically loaded regimes by studying extensions of the well-known square-root safety staffing rule used in the Quality-and-Efficiency-Driven (QED) regime

Modelling for evaluations of call center for public traffic and transport systems

This paper is dealing with functional organization of a call center based on human operator work. Due to significant fluctuations of user demands during the day and from day to day, the determination of required number of agents appears as actual giving the opportunities for efficient management. The purpose of this paper is to develop a mathematical model for optimal resource allocation in a call center in order to provide a satisfactory quality of service at all times, without having more agents than necessary. The objective is to find the best staffing levels or schedule that minimizes the daily costs while satisfying all constraints. To solve this problem, we propose here a two-level dynamic programming (DP) algorithm that determines the required staffing levels by shifts. The algorithm enables optimal allocation of available human resources such that the operation costs are reduced as much as possible. The practical sample is demonstrated in a case of a call center for public traffic and transport systems in metropolitan. The results comparison for different shifts duration is performed