Nearest Neighbour Algorithms for Forecasting Call Arrivals in Call Centers

Companies and governments often rely on call centers to provide service to their customers. The call center industry is of great economic interest; It is rapidly expanding, in terms of workforce and economic scope [1]. Because of its importance a lot of studies have been, and are still being, conducted on modelling call centers. These models are being developed to help understand the performance of call centers under different conditions. This understanding can then be used to cost effectively control the call center. Often call centers need to determine how to assign manpower (agents, in call center terminology) to reach predefined service level goals. These goals are often defined as, 80% of all calls answered within a waiting time of 20 seconds, or an average waiting time of x seconds. Call centers want to reach these goals with minimal costs (e.g., loan wages, overhead costs). Stochastic queuing models are used to model call centers. Frequently used models, using Kendall’s notation, are the M/M/c and the M/M/c/N. The first letter M denotes that arrivals to the call center are according to the (Markovian/memoryless) Poisson process. The second M denotes that service time distribution is exponential (Markovian/memoryless). The third term denotes the number of servers available to handle incoming calls. The fourth term denotes the total capacity of the system, that is the number of servers plus the number of places in the queue. When the system has an infinite queue the fourth term is often omitted. These are the basic properties of a queuing system used to model call centers. Calls arrive at the system with a certain rate λ. They then get routed to a server if there is an idle server, or they get routed to the queue until a server becomes idle. Servers handle their call at a certain rate μ and become available for the next call when they have handled their previous call. From these models we can derive several key performance aspects such as, the average waiting time, the average server utilization, the percentage of callers that have to wait less than 20 seconds, etc. Various variations to these queueing frameworks are possible, including adaptations to the model that: handle servers with different skills, callers that abandon when they have waited for a certain amount of time, etc. However, this project is not about adapting or improving stochastic queueing models, so the interested reader is referred to [1]. The models described above assume a fixed arrival rate λ. When we use the model on a particular day as a whole the results will be unreliable; this is because the call arrival rate λ in call centers varies over the day. Green, Kolesar