The impact of line-sitting on a two-server queueing system

In the presence of multiple lines, customers can often occupy the lines simultaneously with the help of someone else, so as to reduce their wait times. To understand the impact of such line-sitting behavior on the service system with multiple lines, we establish a queueing game-theoretic model to capture the interactions among customers, line-sitting firm and service provider. In particular, we consider a congested-prone service system with two dedicated queues, where arriving customers can join the two queues simultaneously by hiring a line-sitter to wait in one of the line on behalf of them, enabling them to receive service in any one of the queues. Our main results are as follows. First, contrary to our conventional wisdom that line-sitting firm could be more profitable when the system is more congested, we find instead that a queue with an intermediate demand volume can be most susceptible to line-sitting, whereas queues with either a very small or a very large demand volume may not be financially attractive to line-sitters. Second, our result discloses that the provision of line-sitting service in multiple lines can efficiently increase the system throughput. In the short run, both revenue of service provider and the customer surplus can be improved with the provision of line-sitting, which leads to a win-win situation. However, in the long run, line-sitting will stimulate a higher service fee charged by the service provider, reversing its short-run beneficial effect on customers, which results in a lower customer surplus. To restore the efficiency of line-sitting, we propose a centralized regulation policy from the perspective of social planner to maximize the social welfare without detriment to the customer population.