关键词: 排队系统, 不可靠服务台, 有限理性, 定价, 服务速度

Abstract: Customer-intensive service systems are common in our daily life, such as personal care, healthcare and legal consulting. In such service systems, providing professional service requires a longer service time, which can increase customer satisfaction but also increase their waiting time. Therefore, setting an appropriate service rate is critical. When customers arrive at the service system, they decide whether to join the system based on their utility of entering the system. Due to customer limited cognitive ability, customers are usually boundedly rational and they cannot accurately estimate the utility of joining. They make the joining decisions according to their perceived service value and waiting cost. Further, servers are usually unreliable in reality and they may break down when providing service. So in this paper, we consider the customer-intensive service systems with boundedly rational customers and unreliable servers, and study the dilemma of service speed and service quality from the perspective of the service providers.
We consider a market with multiple competing service providers and each service facility is modeled by an M/M/1 queue with an unreliable server. When the server is working, it may break down. If the service of one customer is interrupted by the server's breakdown, the interrupted customer will wait in the system to resume service after the server is repaired. We assume the time between failures and the maintenance time follow exponential distributions. For the boundedly rational customers, we assume the random error in customer estimating the utility of joining follows a Gumbel distribution. Boundedly rational behavior of customers is then characterized by a logit choice model and we give their probability of choosing each server. In monopolistic and competitive situations, we investigate the revenue maximization problem of the service providers and consider the trade-off of revenue-optimal pricing and service rate. By adopting the sequential optimization approach, we derive the revenue-optimal decisions and prove their uniqueness. By comparing the optimal strategies under the two situations, we further study the effect of competition on customers' behavior, revenue-optimal decisions and the social welfare. Lastly, since customers are boundedly rational, they may enter the system even if their actual utility of joining is negative. So we study the sign of customer actual utility under the revenue-optimal decisions and give the condition that customer actual utility is positive.
By making comparisons between monopolistic and competitive situations, we find that competition may reduce the market share of each firm, but the total market share increases. Under competition, each firm sets a lower service rate to increase the service quality, but the manager may simultaneously raise the service price. Meanwhile, the social welfare increases in the competitive situation. Thus, in reality, the manager can take measures to encourage benign competition in the market, such as, providing compensation for enterprises to enter the market. From the perspective of customers, we find that when the market size is large enough, the revenue-optimal strategies lead to a negative utility for boundedly rational customers who enter the service system; however, when the market size is smaller, the revenue-optimal strategies can ensure a positive utility for customers. Similarly, there also exists a threshold of the failure rate such that customer actual utility of joining is positive when the failure rate is less than the threshold. The sign of customer actual utility changes from positive to negative with the increase of failure rate. Our work enriches the literature research on customer-intensive service systems and the findings in this paper provide a theoretical basis to optimize service operations in a competitive environment.
In this paper, we adopt the M/M/1 queue to model the customer-intensive service system and its tractability allows us to investigate the revenue-optimal decisions of the service providers. But the stylish model limits its practical applications. In the future we will extend this research to the queue model with general service times. Another extension is to characterize the boundedly rational behavior of customers by other methods rather than the logit choice model.

Key words: queueing system, unreliable server, bounded rationality, pricing, service rate