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We study the problem of optimal information sharing in the context of a service system. In particular, we consider an unobservable single server queue offering a service at a fixed price to a Poisson arrival of delay-sensitive customers. The service provider can observe the queue, and may share information about the state of the queue with each arriving customer. The customers are Bayesian and strategic, and incorporate any information provided by the service provider into their prior beliefs about the queue length before making the decision whether to join the queue or leave without obtaining service. We pose the following question: which signaling mechanism and what price should the service provider select to maximize her revenue? We formulate this problem as an instance of Bayesian persuasion in dynamic settings. The underlying dynamics make the problem more difficult because, in contrast to static settings, the signaling mechanism adopted by the service provider affects the customers' prior beliefs about the queue (given by the steady state distribution of the queue length in equilibrium). The core contribution of this work is in characterizing the structure of the optimal signaling mechanism. We summarize our main results as follows. (1) Structural characterization: Using a revelation-principle style argument, we find that it suffices to consider signaling mechanisms where the service provider sends a binary signal of "join" or "leave", and under which the equilibrium strategy of a customer is to follow the service provider's recommended action. (2) Optimality of threshold policies: For a given fixed price for service, we use the structural characterization to show that the optimal signaling mechanism can be obtained as a solution to a linear program with a countable number of variables and constraints. Under some mild technical conditions on the waiting costs, we establish that there exists an optimal signaling mechanism with a threshold structure, where service provider sends the "join" signal if the queue length is below a threshold, and "leave" otherwise. (In addition, at the threshold, the service provider randomizes.) For the special case of linear waiting costs, we derive an analytical expression for the optimal threshold i terms of the two branches of the Lambert-W function. (3) Revenue comparison: Finally, we show that with the optimal choice of the fixed price and using the corresponding optimal signaling mechanism, the service provider can achieve the same revenue as with the optimal state-dependent pricing mechanism in a fully-observable queue. This implies that in settings where state-dependent pricing is not feasible, the service provider can effectively use optimal signaling (with the optimal fixed price) to achieve the same revenue.
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Should Opportunists Be Encouraged? Optimal Decisions in Hybrid Cloud Service Systems
This paper investigates a hybrid service system with a cloud server and an in-house server. We consider two different scenarios: a hybrid service system with orbit space and a hybrid service system without orbit space. In the hybrid service system with orbit space, customers who fail to enter the cloud server can choose to join the in-house subsystem or to enter an orbit space and retry the cloud server. An admission control mechanism based on queue-length limitation is adopted to adjust whether the cloud service resources are open to customers. When the cloud server cannot be accessed immediately, some customers send their jobs to the in-house subsystem, while others (called opportunists) try to send their jobs to the cloud server again. We obtain the optimal queue-length limitation for a given retrial rate. The service provider and customers are different stakeholders, and their market forces are also different. Therefore, it is more realistic to explore the game relationship between them by using dynamic game theory. We can also explore the joint optimums of the queue-length limitation and the retrial rate in the framework of the Stackelberg game. Finally, by comparing with the hybrid service system without orbit space, we discuss the significance of the existence of orbit space, and gain management insights. It is found that the existence of opportunists may benefit the service provider, although they significantly harm social interests, regardless of whether they are cooperative or non-cooperative; therefore, opportunists are encouraged in some situations. Numerical analysis shows that adding a retrial orbit to a hybrid cloud service system with certain input parameters may even more than triple the service provider’s revenue.
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- Award ID(s):
- 2318662
- PAR ID:
- 10544819
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Network and Service Management
- Volume:
- 21
- Issue:
- 3
- ISSN:
- 1932-4537
- Page Range / eLocation ID:
- 3330-2243
- Subject(s) / Keyword(s):
- Cloud service queueing-game optimal decision hybrid service system Stackelberg game.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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