Measuring the variance of customer waiting time in service operations

Purpose: Waiting lines and delays have become commonplace in service operations. As a result, customer waiting time guarantee is a widely used competition strategy in service industries. To implement waiting time guarantee strategy, managers need to not only know the average of waiting time, but also the variance around average waiting time. This paper aims to discuss these issues. Design/methodology/approach: This research provides a mathematically exact expression for the coefficient of variation of waiting time for Markov queues. It then applies the concept of isomorphism to approximate the variance of customer waiting time in a general queue. Simulation experiments are conducted to verify the accurate approximations. Findings: A significant feature of the approximation method is that it is mathematically tractable and can be implemented in a spreadsheet format. It provides a practical way to estimate the variance of customer waiting time in practice. The results demonstrate the usefulness of the queuing models in providing guidance on implementing appointment scheduling and waiting time guarantee strategy. Also, the spreadsheet can be used to conduct what-if analysis by inputting different parameters. Originality/value: This paper develops a simple, easy-to-use spreadsheet model to estimate the standard deviation of waiting time. The approximation requires only the mean and standard deviation or the coefficient of variation of the inter-arrival and service time distributions, and the number of servers. A spreadsheet model is specifically designed to analyze the variance of waiting time.