Approximating multiple class queueing models with loss models

Multiple class queueing models arise in situations where some flexibility is sought through pooling of demands for different services. Earlier research has shown that most of the benefits of flexibility can be obtained with only a small proportion of cross-trained operators. Predicting the performance of a system with different types of demands and operator pools with different skills is very difficult. We present an approximation method that is based on equivalent loss systems. We successively develop approximations for the waiting probability, The average waiting time and the service level. Our approximations are validated using a series of simulations. Along the way we present some interesting insights into some similarities between queueing systems and equivalent loss systems that have to our knowledge never been reported in the literature.

Dynamic routing policies for multi-skill 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. © 2009 Cambridge University Press

Establishing agent staffing levels in queueing systems with cross-trained and specialized agents

The determination of the right number of servers in a multi-server queueing system is one of the most important problems in applied queueing theory. The problem becomes more complex in a system that consists of both cross-trained and specialized servers. Such queueing systems are readily found in the call centres (also called contact centres) of financial institutions, telemarketing companies and other organizations that provide services to customers in multiple languages. They are also found in computer network systems where some servers are dedicated and others are flexible enough to handle various clients' requests. Over-staffing of these systems causes increased labour costs for the underutilized pool of agents on duty, while under-staffing results in reduced revenue from lost customers and an increase in queue times. The efficient design and analysis of these systems helps management in making better staffing decisions. This thesis aims to develop models for establishing agent staffing levels in organizations with cross-trained and specialized staff with a view to minimizing cost and maintaining a desirable customer satisfaction. The work investigates the effect of various traffic loads on the number of agents required and the cost. It also considers how using specialized agents, flexible agents and a combination of both categories of agents affects the system. It uses a contact centre that has agents with monolingual, bilingual and trilingual (English, French and Spanish) capabilities to do the study

A Clustered Overflow Configuration of Inpatient Beds in Hospitals

Problem Definition: The shortage of inpatient beds is a major cause of delays and cancellations in many hospitals. It may also lead to patients being admitted to inappropriate wards, whereby resulting in a lower quality of care and a longer length of stay. Academic/Practical Relevance: Investment in additional beds is not always feasible. Instead, new and creative solutions for a more efficient use of existing resources must be sought. Methodology: We propose a new configuration of inpatient beds which we call the clustered overflow configuration. In this configuration, patients who are denied admission to their primary wards as a result of beds being fully occupied are admitted to overflow wards, with each designated to serve overflows from a certain subset of specialties and providing the same quality of care as in primary wards. We propose two different formulations for partitioning and bed allocation in the proposed configuration: one minimizing the sum of average daily costs of turning patients away and nursing teams, and another minimizing the numbers turned away subject to nursing cost falling below a given threshold. We heuristically solve instances from both formulations. Results: Applying the models to real data shows that the configurations obtained from our models compare very well with the other configurations proposed in the literature, provided that patients' willingness to wait is relatively short. Managerial Implications: The proposed configuration provides the combined advantages of the dedicated configuration, wherein patients are only admitted to their primary wards, and the exible configuration, in which all specialties share a single ward. On the other hand, it restricts the adverse impacts of pooling and minimizes cross-training costs through appropriate partitioning and bed allocation. As such, it serves as a viable alternative to existing inpatient configurations

Time-dependent performance approximation of truck handling operations at an air cargo terminal

This paper provides an analytical solution for the time-dependent performance evaluation of truck handling operations at an air cargo terminal. The demand for loading and unloading operations is highly time-dependent and stochastic for two classes of trucks. Two heterogeneous handling facilities with multiple servers are available to handle trucks assuming exponentially distributed processing times. Trucks are routed to a handling facility depending on the current state of the system upon arrival. To approximate the time-dependent behavior of such heterogeneous queueing systems, we develop a stationary backlog-carryover (SBC) approach. A numerical study compares this approach with simulations and demonstrates its applicability to real-world input data