Waiting Time Control Chart for M/G/1 Retrial Queue

Abstract

Retrial queues are used extensively to model many practical problems in service systems, call centers, data centers, and computer network systems. The average waiting time is the main observable characteristic of the retrial queues. Long queues may cause negative impacts such as waste of manpower and unnecessary crowding leading to suffocation, and can even cause trouble for customers and institutions. Applying control chart technology can help managers analyze customers’ waiting times to improve the effective performance of service and attention. This paper pioneers the developing and detailed study of a waiting time control chart for a retrial queue with general service times. Two waiting time control charts, the Shewhart control chart, and a control chart using the weighted variance method are constructed in this paper. We present three cases for the Shewhart control chart in which the service time obeys special distributions, such as exponential, Erlang, and hyper-exponential distributions. The case of an exponentially distributed service time is also presented for the control chart using the weighted variance method. Based on the numerical simulations conducted herein, managers can better monitor and analyze the customers’ waiting times for their service systems and take preventive measures.

Keywords

• waiting time
• control chart
• retrial queue
• general service times