Sandjai Bhulai

A queueing model for call blending in call centers

Call centers that apply call blending obtain high-productivity and high-service levels by dynamically mixing inbound and outbound traffic. We show that agents should be assigned to outbound calls if the number of available agents exceeds a certain threshold. This control policy is optimal for equal service time distributions and a very good approximation otherwise.

Simple Methods for Shift Scheduling in Multiskill Call Centers

This paper introduces a new method for shift scheduling in multiskill call centers. The method consists of two steps. First, staffing levels are determined, and next, in the second step, the outcomes are used as input for the scheduling problem. The scheduling problem relies on a linear programming model that is easy to implement and has short computation times, i.e., a fraction of a second. Therefore, it is useful for different purposes and it can be part of an iterative procedure: for example, one that combines shifts into rosters.

A Simple Staffing Method for Multiskill Call Centers

We study a simple method for staffing in multiskill call centers. The method has short computation times and determines nearly optimal staffing levels. It is in both views competitive to other methods from the literature. Because of the fast and accurate performance of the method, many different scenarios can be analyzed, and our method can be used for both tactical and strategic capacity management decisions.

Dynamic routing policies for multiskill call centers

We consider the problem of routing calls dynamically in a multiskill call center. Calls from different skill classes are offered to the call center according to a Poisson process. The agents in the center are grouped according to their heterogeneous skill sets that determine the classes of calls they can serve. Each agent group serves calls with independent exponentially distributed service times. We consider two scenarios. The first scenario deals with a call center with no buffers in the system, so that every arriving call either has to be routed immediately or has to be blocked and is lost. The objective in the system is to minimize the average number of blocked calls. The second scenario deals with call centers consisting of only agents that have one skill and fully cross-trained agents, where calls are pooled in common queues. The objective in this system is to minimize the average number of calls in the system. We obtain nearly optimal dynamic routing policies that are scalable with the problem instance and can be computed online. The algorithm is based on one-step policy improvement using the relative value functions of simpler queuing systems. Numerical experiments demonstrate the good performance of the routing policies. Finally, we discuss how the algorithm can be used to handle more general cases with the techniques described in this article.

Optimal patient and personnel scheduling policies for care-at-home service facilities

In this paper we study the problem of personnel planning in care-at-home facilities. We model the system as a Markov decision process, which leads to a high-dimensional control problem. We study monotonicity properties of the system and derive structural results for the optimal policy. Based on these insights, we propose a trunk reservation heuristic to control the system. We provide numerical evidence that the heuristic yields close to optimal performance, and scales well for large problem instances.

On structural properties of the value function for an unbounded jump Markov process with an application to a processor sharing retrial queue

The derivation of structural properties for unbounded jump Markov processes cannot be done using standard mathematical tools, since the analysis is hindered due to the fact that the system is not uniformizable. We present a promising technique, a smoothed rate truncation method, to overcome the limitations of standard techniques and allow for the derivation of structural properties. We introduce this technique by application to a processor sharing queue with impatient customers that can retry if they renege. We are interested in structural properties of the value function of the system as a function of the arrival rate.

Optimal resource allocation in survey designs

Resource allocation is a relatively new research area in survey designs and has not been fully addressed in the literature. Recently, the declining participation rates and increasing survey costs have steered research interests towards resource planning. Survey organizations across the world are considering the development of new mathematical models in order to improve the quality of survey results while taking into account optimal resource planning. In this paper, we address the problem of resource allocation in survey designs and we discuss its impact on the quality of the survey results. We propose a novel method in which the optimal allocation of survey resources is determined such that the quality of survey results, i.e., the survey response rate, is maximized. We demonstrate the effectiveness of our method by extensive numerical experiments.

Dynamic thread assignment in web server performance optimization

Popular web sites are expected to handle huge number of requests concurrently within a reasonable time frame. The performance of these web sites is largely dependent on effective thread management of their web servers. Although the implementation of static and dynamic thread policies is common practice, remarkably little is known about the implications on performance. Moreover, the commonly used policies do not take into account the complex interaction between the threads that compete for access to a shared resource. We propose new dynamic thread-assignment policies that minimize the average response time of web servers. The web server is modeled as a two-layered tandem of multi-threading queues, where the active threads compete for access to a common resource. This type of two-layered queueing model, which occurs naturally in the performance modeling of systems with intensive software-hardware interaction, are on the one hand appealing from an application point of view, but on the other hand are challenging from a methodological point of view. Our results show that the optimal dynamic thread-assignment policies yield strong reductions in the response times. Validation on an Apache web server shows that our dynamic thread policies confirm our analytical results.

Gamma frailty model for linkage analysis with application to interval-censored migraine data

For many diseases, it seems that the age at onset is genetically influenced. Therefore, the age-at-onset data are often collected in order to map the disease gene(s). The ages are often (right) censored or truncated, and therefore, many standard techniques for linkage analysis cannot be used. In this paper, we present a correlated frailty model for censored survival data of siblings. The model is used for testing heritability for the age at onset and linkage between the loci and the gene(s) that influence(s) the survival time. The model is applied to interval-censored migraine twin data. Heritability (obtained from the frailties rather than actual onset times) was estimated as 0.42; this value was highly significant. The highest lod score, a score of 1.9, was found at the end of chromosome 19.

A Multiphased Approach for Modeling and Analysis of the BitTorrent Protocol

BitTorrent is one of the most popular protocols for content distribution and accounts for more than 15% of the total Internet traffic. In this paper, we present an analytical model of the protocol. Our work differs from previous works as it models the BitTorrent protocol specifically and not as a general file-swarming protocol. In our study, we observe that to accurately model the download process of a BitTorrent client, we need to split this process into three phases. We validate our model using simulations and real-world traces. Using this model, we study the efficiency of the protocol based on various protocol-specific parameters such as the maximum number of connections and the peer set size. Furthermore, we study the relationship between changes in the system parameters and the stability of the protocol. Our model suggests that the stability of BitTorrent protocol depends heavily on the number of pieces a file is divided into and the arrival rate of clients to the network.