Managing a service system with social interactions: Stability and chaos

This paper investigates the dynamic behavior of a service system in terms of the arrival rate in the steady state under the influence of social interactions. Customers are backward looking and rational when making purchasing decisions. Existing customers’ re‐purchasing decisions are based on their experienced utility – a function of the average waiting time and their expected utility. Potential customers are attracted through social interactions with existing customers. It is shown that the arrival rate of the system in the steady state can exhibit stability, periodic cycles, or chaos due to the effect of social interactions and customers’ purchasing behavior. Two examples based on an M/M/1 queueing system illustrate the role of social interactions and the effect of service rates on the stability of the arrival rate in the steady state. The result highlights the dynamical complexity of a simple service system under the impact of customers’ behavioral factors, or social interactions. It suggests a new perspective to managing service operations whereby social interactions may play a critical role in the fluctuations of demand.