Chat service in a multichannel system under competition where customers are boundedly rational

Many service systems in various type of industry provide services via chat technologies. This type of service system is characterized by an interesting combination of properties. First, the customer is actively involved in service execution, since the service is comprised of responses of the server and the customer to each other, until the customer's request is satisfied. In addition, in such a system, the service can be provided by a single server in a parallel manner to a number of customers. Motivated by these and others interesting properties of the chat service, we formulate and analyze the stochastic queueing system as a two-dimensional quasi-birth-and-death process and derive its steady-state probabilities using matrix geometric methods. By means of economic analysis, we provide a scheme for deriving the optimal capacity of parallel chats and the optimal response effort that should be made by the server, considering that higher effort lengthens the response time but increases the probability of successful service completion. We next investigate a queueing game that considers a multi-channel service system consisting of a chat service and a traditional multi-server call center, and we consider strategic customers under both a centralized and a decentralized scenario. We show that competition between service channels may lead to lower service utilization even though customers enjoy higher expected utility. Finally, customer bounded rationality is considered and it is shown that customers who are less rational may enjoy higher utility. Sensitivity analyses are conducted for all scenarios.