Individual and social customers’ joining strategies in a two-stage service system when discount is offered to users of smartphone application

The use of smartphone applications (APP) for the purchase of services, such as food, flights or household goods, is becoming an increasingly common practice. This practice generates two- phase service systems composed of (i) an ordering phase operated by several servers (under a dynamic vacation policy), and (ii) a following preparation phase. Upon arrival, strategic customers can either join an observable first-stage queue and then continue to a partially unobservable second-stage queue, or balk never to return. In contrast, APP users register their order in advance, skip the first phase and join directly the second-stage queue. Each server stationed at the first service stage takes a ‘vacation’ when a server-dependent queue size drops below a given value. An individual strategic customer is concerned only with his/her net utility, while a social customer is concerned with the overall social welfare. Each type of customers follows a threshold-joining policy. However, contrary to Naor's seminal model, we show that under such a scenario, the social joining threshold is not always smaller than the individual one, and that several equilibrium thresholds may exist. We analyze the profit optimization problem of the service system's manager when a price discount is offered to potential APP users and show that it may increase manager's profit, reduce customers’ sojourn times, reduce the first-stage queue size, and reduce the number of servers required to operate the first-stage queue. Numerical examples are presented.