When more capacity creates more congestion: The role of risk aversion

Abstract

A fundamental principle in operations management holds that increasing the number of servers reduces delays in service systems. To date, no mechanism has been identified that could reverse this effect. We propose, however, that risk aversion can cause increased service capacity to intensify congestion. We study an unobservable $M/M/s$ queue where risk-averse customers choose whether to join based on their anticipated waiting time. We show that, in equilibrium, demand, expected waiting time, expected sojourn time, and the probability of waiting all increase with the number of servers, and that these effects are stronger for more risk-averse customers. We further uncover the mechanism behind this phenomenon: adding servers makes delays less risky (in the sense of second-order stochastic dominance), which increases the sensitivity of demand to capacity as customers become more risk-averse. These patterns are more prevalent in small systems and fade as the system grows. They can also persist when customers differ in their degree of risk aversion, when capacity is increased by raising service speed, and when the system is observable. Our findings reveal a novel trade-off created by customer risk aversion: expanding capacity attracts more customers, but also exacerbates congestion. A manager aiming to reduce waiting times may therefore prefer to de-pool service capacity instead of following the standard approach of pooling, while increasing capacity in the resulting smaller systems to preserve total throughput. When the objective is to maximize profitability, our results further suggest that the cost of additional servers may be offset by the associated increase in revenue when customers are sufficiently risk-averse.