Effects of state-dependent balking on multi-server non-stationary queueing systems

Abstract

A combination of discrete-time modelling and theoretical analysis is used to develop an easy-to-use Normal approximation for the time-dependent behaviour of multi-server queueing systems subject to state-dependent balking. Key findings that underpin the approximation are that time lags between peaks in arrival rates and congestion levels can be ignored; queue behaviour is insensitive to distribution of service time beyond its mean; and distribution of number in the system is near Normal. This model is then used to derive valuable management implications for service-orientated systems where delays are frequent and abandonments are an important feature. Key insights are that such systems can often adopt very ‘sub-optimal’ behaviour, and that customer impatience can be very beneficial where management wishes to improve system performance. ‘Optimal’ performance is defined, and practical measures for queue managers to move system performance towards ‘optimality’ are identified.

Keywords:

• time-dependent analysis
• discrete-time
• state-dependent balking
• multi-server queues