


Research
 Performance Analysis of Call Centers
Typically a call center consists of telephone trunk lines, an automatic call distributor, and sales agents. Customers usually dial a special number. If a trunk line is free, the customer seizes it, otherwise the call is lost. Once the trunk line is seized, the caller is instructed to choose among several options. After completing the instructions, the call is routed to an available agent. If all agents are busy, the call is queued until one is free. Queuing and queuing network models developed to address the design issue assume that one knows how to estimate the basic parameters of the models. For example, it is common to assume that call arrivals are Poisson with constant rate and the call handling times are exponentially distributed. These assumptions are often violated in realistic call centers. Time of day, day of the week and weekly effects need to be taken into account. Queuing models with time varying rates have been proposed and analyzed in the literature but not much attention has been paid to estimating the parameters of the arrival process. A recent investigation by one of or Master's student has revealed that modeling call load process via a Poisson process with piecewise constant and linear rates does not work very well for a particular call center data set. Techniques based on spline regression perform well when compared to other techniques. Our investigation has also revealed that in addition to the stochastic variability in the arrival process, there is an additional uncertainty about the model parameters. We propose to investigate a model in which when the arrival process is modeled as a Poisson process with constant rate, the rate itself is a random variable. The variation of call volume over time can be attributed to events such as special advertising or promotion or introduction of new products. We have also assumed that the processing times, call holding time and abandonment times are exponentially distributed. Recently one of our Master's student has investigated the adequacy of the exponential assumption for holding times by analyzing data from a contact centre. We see that lognormal distributions fit very well to various call holding times. Since queues with lognormal service times are very hard to analyze, we looked into fitting a phase type distribution with different phases to the same data set. It was found that phase type distributions of different orders fit our data, and this leads to our next problem namely, when can one approximate a lognormal distribution by a phasetype distribution? Are there limit theorems to support such an approximation? We will investigate the condition under which such an approximation is appropriate.
