Expected performance of a queueing system with ancillary activities

Many service organizations follow a scheduling policy whereby employees alternate between direct customer service (e.g. bank deposits and withdrawals) and an ancillary activity (e.g. bookkeeping, paperwork). When queues are short, employees are diverted to ancillary activities; when queues become long, employees return to customer service. This paper evaluates trade-offs between the system objectives of (1) minimizing customer delay, (2) minimizing teller idle time, and (3) minimizing the disruption of ancillary activities, for queueing systems with ancillary activities. Customers are assumed to arrive by a stationary Poisson process, and service times are exponential random variables. In terms of objectives (1) and (3), the best of four policies studied is to add a server when the queue size per server reaches a maximum and remove a server when the queue size equals zero. The difference in teller idle time between the policies is generally small, particularly when the traffic intensity is large.