Eran Simhon

Game-theoretic analysis of advance reservation services

In many services, such as cloud computing, customers have the option to make reservations in advance. However, little is known about the strategic behavior of customers in such systems. In this paper, we use game theory to analyze several models of time-slotted systems in which customers can choose whether or not making an advance reservation of server resources in future time slots. Since neither the provider nor the customers know in advance how many customers will request service in a given slot, the models are analyzed using Poisson games, with decisions made based on statistical information. The games differ in their payment mechanisms, and the main objective is to find which mechanism yields the highest average profit for the provider. Our analysis shows that the highest profit is achieved when advance reservation fees are charged only from customers that are granted service. Furthermore, informing customers about the availability of free servers prior to their decisions do not affect the providers profit in that case.

A game-theoretic perspective on advance reservations

Advance reservation is a fundamental paradigm for resource allocation. It is employed in various economic sectors, including cloud computing and communication networks. Although advance reservations are widespread, little is known about the strategic behavior of users facing the decision whether to reserve a resource in advance or not. In this article, we present a game-theoretic framework, called advance reservation (AR) games, to analyze this strategic behavior. We use AR games to analyze the impact of pricing, charging, and information sharing policies on the economic equilibria of the system and on its dynamic behavior. The analysis yields several insights on how a service provider should design a system that supports advance reservations.

Advance Reservation Games and the Price of Conservatism

Advance reservation (AR) services form a pillar of many branches of the economy, e.g., transportation, lodging, dining, and health care. There has also been increased interest in applying AR in cloud computing systems [1]. For instance, Moab Workload Manager [2] and IBM Platform Computing Solutions [3] support AR. In both of these packages, an administrator can decide whether or not to enable AR and define an AR pricing scheme. In most systems supporting AR, customers can choose whether making AR or not. Since the payoff of each customer is affected by decisions of other customers, it is natural to analyze the behavior of such systems as strategic games. In this work, we study a strategic non-cooperative game, referred to as an advance reservation game. In this game, players (customers) can reserve future resources in advance for a fixed reservation fee C. We consider a slotted loss system with N servers where customers are not flexible, i.e., they leave the system if they cannot be served at their desired time slots. Customers are not informed of the state of the system (i.e., the number of unreserved servers) prior to attempting a reservation. Thus, a customer opting not to make a reservation lowers its chance of finding a server available at the desired time. The number of customers in each slot is an i.i.d. Poisson random variable with parameter λ [4]. Customers have different lead times, where the lead time of a customer is defined as the time elapsing between its arrival and the slot starting time. Each customer only knows its own lead time. However, all lead times are derived from the same continuous distribution known by both the provider and the customers. In [5], we derive the equilibria structure of AR games. We show that for any C > 0, only two types of equilibria are possible. In the first type, none of the customers, regardless of their lead times, makes AR (non-make-AR equilibrium). In the second type, only customers with lead time greater than some threshold make AR (threshold equilibrium). Furthermore, we establish the existence of three different ranges of fees, such that if C falls in the first range only threshold equilibria exist, in the second range both threshold equilibria and a none-make-AR equilibrium exist, and in the third range only a none-make-AR equilibrium exists. In many cases, the fee C that maximizes the providers profit lies in the second range. However, setting up a fee in that range carries also the risk of zero profit for the provider. Therefore, in order to properly set the AR fee, the provider should consider both the fee yielding the maximum possible profit and the fee yielding the maximum guaranteed profit. A guaranteed profit can be only achieved using fees falling within the first range. In this work, we introduce the concept of price of conservatism (PoC), which corresponds to the ratio of the maximum possible profit to the maximum guaranteed profit, and analyze it in different regimes. A greater PoC indicates greater potential profit loss if the provider opts to be conservative. First, we analyze a single-server regime, where we prove that for any fee the equilibrium is unique (the second range collapses in that case). Hence, PoC = 1 and the provider experiences no loss. Next, we analyze a many-server regime where λ = αN and N → ∞. We distinguish between the cases of overloaded and underloaded systems (i.e., α > 1 and α < 1 respectively). For the overloaded case, we show that PoC = α/(α--1). Hence, the price of conservatism increases in an unbounded fashion as α approaches one from above. Finally, for the underloaded case, we show that both the maximum and guaranteed profits converge to zero.

Optimal information disclosure policies in strategic queueing games

Information about queue length is an important parameter for customers who face the decision whether to join a queue or not. In this paper, we study how optimal information disclosure policies can be used by a service provider of an M / M / 1 queue to increase its revenue. Our main contribution is showing that the intuitive policy of informing customers about the current queue length when it is short and hiding this information when it is long is never optimal.

Smart parking pricing: A machine learning approach

Crowded streets are a major problem in large cities. A large part of the problem stems from drivers seeking on-street parking. Cities such as San Francisco, Los Angeles and Seattle have tackled this problem with smart parking systems that aim to maintain the on-street parking occupancy rates around a target level, thus ensuring that empty spots are spread across the city rather than clustered in a single area. In this study, we use the San Franciscos SFpark system as a case study. Specifically, in each given parking area, the SFpark uses occupancy rate data from the previous month to adjust the price in the current month. Instead, we propose a machine learning approach that predicts the occupancy rate of a parking area based on past occupancy rates and prices from an entire neighborhood (which covers many parking areas). We further formulate an optimization problem for the prices in each parking area that minimize the root mean squared error (RMSE) between the predicted occupancy rates of all areas in the neighborhood and the target occupancy rates. This approach is novel in that 1) it responds to a predicted level of occupancy rate rather than past data and 2) it find prices that optimize the total occupancy rate of all neighborhoods, taking under account that prices in one area can impact the demand in adjacent areas. We conduct a numerical study, using data collected from the SFpark study, that shows that the prices obtained from our optimization lead to occupancy rates that are very close to the desired target level.

Advance Reservation Games

Advance reservation (AR) services form a pillar of several branches of the economy, including transportation, lodging, dining, and, more recently, cloud computing. In this work, we use game theory to analyze a slotted AR system in which customers differ in their lead times. For each given time slot, the number of customers requesting service is a random variable following a general probability distribution. Based on statistical information, the customers decide whether or not to make an advance reservation of server resources in future slots for a fee. We prove that only two types of equilibria are possible: either none of the customers makes AR or only customers with lead time greater than some threshold make AR. Our analysis further shows that the fee that maximizes the provider’s profit may lead to other equilibria, one of which yields zero profit. In order to prevent ending up with no profit, the provider can elect to advertise a lower fee yielding a guaranteed but smaller profit. We refer to the ratio of the maximum possible profit to the maximum guaranteed profit as the price of conservatism. When the number of customers is a Poisson random variable, we prove that the price of conservatism is one in the single-server case, but can be arbitrarily high in a many-server system.

On the Impact of Sharing Information in Advance Reservation Systems

Services that allow advance reservations (AR) over the Internet differ in the information provided to customers about future availability of servers. In some services, customers observe the exact number of currently available servers prior to making decisions. In other services, customers are only alerted when a few servers remain available, while there are also services in which no information whatsoever is shared about the availability of servers. Examples for the first case can be found in entertainment services, where customers are allowed to choose their seats and observe the exact number of available seats. Examples for the second case can be found in lodging reservations websites, such as Booking.com, that alert potential customers only when a few available rooms are left. Booking of airline tickets is an example of the third case where no information is provided (typically, customers can choose seats but only after buying a ticket). In recent years, research on the impact of information on different queueing systems has emerged (see [1], for example). However, not much is known about the impact of information in systems that allow advance reservations. Our goal is to understand how di?erent information sharing policies affect the decision of customers whether to reserve a resource in advance or not. Towards this end, we define a game, in which customers either reserve a resource in advance or avoid advance reservation and take the risk that the resource will not be available when needed. Making advance reservation is associated with a fixed cost. This cost can be interpreted as a reservation fee, as the time or resources required for making the reservation, or as the cost of financing advance payment of the service. AR games were introduced in [2] and further investigated in [3]. In the model considered in that paper, customers are not informed about the number of available servers. In contrast, in this present work, we consider a set-up where customers can observe the state of the system prior to making a reservation. We first study a fully-observable game. In this game, customers observe the exact number of available servers. We determine the equilibrium structure and prove the existence and uniqueness of the equilibrium. We then consider a semi-observable game. In this game, the provider informs customers about the number of available servers only if this number is smaller or equal to some threshold. We assume that customers that are not informed realize that the number of available servers is greater than that threshold and take this fact under consideration upon making their decisions. We show that, in this case, there may be multiple equilibria and the number of equilibria depends on the AR cost. Finally, using simulations we show that, on average, the fraction of customers making AR decreases as more information is provided to the customers. More specifically, the fully observable policy yields the lowest number of reservations. In semi-observable policies, the fraction of customers making advance reservation increases as the threshold is lowered, and the best performance is achieved when no information at all is provided. Proofs of the results and more details about the simulation could be found in the working paper copy. There are still many open questions remaining about the impact of sharing information on customers behavior in advance reservation services. Possible directions for further research include systems where customers have incomplete knowledge of statistics, or systems where the provider shares imprecise information.

Distributed strategic mode selection for large-scale D2D communications based on Queue State Information

Device-to-Device (D2D) communication that enables nearby mobiles to directly communicate one with another is a new paradigm aimed at increasing the capacity of next-generation wireless networks. The coexistence of D2D and cellular communication in the same spectrum poses new challenges for resource allocations and interference management in a large-scale wireless system where each mobile strategically selects its mode of communications. This paper formulates a game-theoretic framework to capture the distributed strategic behavior of a large population of mobiles in selecting their mode of communications. In particular, we investigate the impact of Queue State Information (QSI) of the base station (BS) on the mobile decisions, and we show that the common knowledge of QSI can induce bad quality of service for standard cellular traffic, when the capacity of the base station is below a certain threshold. This paradox will be used to guide the design of optimal learning and scheduling algorithms for the coexisting D2D communication networks.

Pricing in dynamic advance reservation games

We analyze the dynamics of advance reservation (AR) games: games in which customers compete for limited resources and can reserve resources for a fee. We introduce and analyze two different learning models. In the first model, called strategy-learning, customers are informed of the strategy adopted in the previous iteration, while in the second model, called action-learning, customers estimate the strategy by observing previous actions. We prove that in the strategy-learning model, convergence to equilibrium is guaranteed. In contrast, in the action-learning model, the system converges only if an equilibrium in which none of the customers makes AR exists. Based on those results, we show that if the provider is risk-averse and sets the AR fee low enough, action-learning yields on average greater profit than strategy-learning. However, if the provider is risk-taking and sets a high AR fee, action-learning provably yields zero profit in the long term in contrast to strategy-learning.

A case study of a shared/buy-in computing ecosystem

Many research institutions are deploying computing clusters based on a shared/buy-in paradigm. Such clusters combine shared computers, which are free to be used by all users, and buy-in computers, which are computers purchased by users for semi-exclusive use. The purpose of this paper is to characterize the typical behavior and performance of a shared/buy-in computing cluster, using data traces from the Shared Computing Cluster (SCC) at Boston University that runs under this paradigm as a case study. Among our main findings, we show that the semi-exclusive policy, which allows any SCC user to use idle buy-in resources for a limited time, increases the utilization of buy-in resources by 17.4%, thus significantly improving the performance of the system as a whole. We find that jobs allowed to run on idle buy-in resources arrive more frequently and run for a shorter time than other jobs. Finally, we identify the run time limit (i.e., the maximum time during which a job is allowed to use resources) and the type of parallel environment as two factors that have a significant impact on the different performance experienced by shared and buy-in jobs.