Wait Time Based Pricing For Queueing Systems
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Wait Time Based Pricing For Queueing Systems
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Author : Chen-An Lin
language : en
Publisher:
Release Date : 2023
Wait Time Based Pricing For Queueing Systems written by Chen-An Lin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
This dissertation studies dynamic pricing in service systems where the system state is defined as the wait time. The first essay studies a single-server queue where customers arrive according to a Poisson process. The service provider announces the price rate and current system wait time to incoming customers, who decide whether to join the queue and determine their service duration. The objective is to maximize either the long-run average revenue or social welfare. The problem is formulated as a continuous-time control model, and we develop an innovative method to obtain the optimal control policy. The optimal dynamic pricing policy reveals the compensation effect, where the service provider lowers the price rate when the wait time exceeds a threshold, in addition to the usual congestion effect. A numerical study demonstrates the superiority of the revenue-maximizing pricing policy over static pricing policies, especially for low arrival rates and impatient customers. The extension to nonlinear pricing and heterogeneous customers yields similar policy insights, showcasing the value of considering customer characteristics in dynamic pricing models. The proposed model can be utilized to design dynamic pricing schemes for fast-charging stations. The second essay addresses a mechanism design problem for a single-server queue with customers arriving according to a Poisson process and possessing private information about their wait time sensitivity. Following a direct mechanism, where the service provider announces the system wait time and offers a menu of options to each arriving customer. By choosing an option or opting out, customers aim to maximize their utility. The objective is to design a mechanism that maximizes the long-run average revenue. The optimal mechanism is wait-time dependent and admits customers with lower wait-time sensitivities. The model reveals strategic complementarity between admission decisions and service times which became the admission threshold, and offered service time decreases as the wait time increases. Comparisons with simpler heuristic mechanisms quantify the value of the optimal mechanism, showing significantly higher revenue generation, particularly for moderate service costs and arrival rates. Modifying service times becomes crucial when considering the different customer types and their interaction with wait time.The third essay investigates a queueing system where the firm strategically determines the release time of each arriving request. We consider a first-come-first-serve single-server system, with customer requests arriving according to a Poisson process. The base model includes two types of customers: impatient and patient, characterized by their privately known service valuations and time sensitivities. The chapter explores the potential of strategically delaying the release of products to improve system performance. It reveals that such a delay occurs when the proportion of impatient customers is high and the system wait time is shorter than the threshold. Importantly, the optimal inflated release time does not vary with the system wait time, facilitating practical implementation. The extension to continuous-type customers confirms the tangible impact of strategic delay on revenue improvement, particularly when faced with uncertainty in the types of arriving requests.
Wait Time Based Pricing For Queues With Customer Chosen Service Times
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Author : Chen-An Lin
language : en
Publisher:
Release Date : 2020
Wait Time Based Pricing For Queues With Customer Chosen Service Times written by Chen-An Lin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
This paper studies a pricing problem for a single-server queue where customers arrive according to a Poisson process. For each arriving customer, the service provider announces a price rate and a system wait time, and the customer decides whether to join the queue, and, if so, the duration of the service time. The objective is to maximize either the long-run average revenue or social welfare. We formulate this problem as a continuous-time control model whose optimality conditions involve solving a set of delay differential equations. We develop an innovative method to obtain the optimal control policy, whose structure reveals interesting insights. The optimal dynamic price rate policy is not monotonic in wait time. In particular, in addition to the congestion effect often reported in the literature, i.e., the optimal price rate increases in the queue length (measured by the wait time in our setting), we find a compensation effect, meaning that the service provider should lower the price rate when the wait time is longer than a threshold. Compared with the prevalent flat pricing policy, our optimal dynamic pricing policy improves the objective value through admission control, which, in turn, increases the utilization of the server. We use a real data set obtained from a public charging station to calibrate our model with an objective of maximizing the average revenue. We find that our optimal pricing policy outperforms the best flat pricing policy, especially when the arrival rate is low and drivers are impatient. Interestingly, our revenue-maximizing pricing policy also improves social welfare over the flat pricing policy in most of the tested cases.
Control Mechanisms In Queueing Systems With Nonlinear Waiting Costs
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Author : Ata Ghareh Aghaji Zare
language : en
Publisher:
Release Date : 2017
Control Mechanisms In Queueing Systems With Nonlinear Waiting Costs written by Ata Ghareh Aghaji Zare and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Operations research categories.
In many queueing systems, customers have been observed to exhibit strategic behavior. Each customer gains a value when receiving a product or getting served and suffers when incurring a delay. We consider a nonlinear waiting cost function to capture the sensitivity of customers toward delay. We investigate customers' behavior and system manager's strategy in two different settings: (1) customers are served in a service system, or (2) they receive a product in a supply chain. In the first model, we study an unobservable queueing system. We consider that customers are impatient, and are faced with decision problems whether to join a service system upon arrival, and whether to remain or renege at a later time. The goal is to address two important elements of queueing analysis and control: (1) customer characteristics and behavior, and (2) queueing control. The literature on customer strategic behavior in queues predominately focuses on the effects of waiting time and largely ignores the mixed risk attitude of customer behavior. Empirical studies have found that customers' risk attitudes, their anticipated time, and their wait time affect their decision to join or abandon a queue. To explore this relationship, we analyze the mixed risk attitude together with a non-linear waiting cost function that includes the degree of risk aversion. Considering this behavior, we analyze individuals' joint balking and reneging strategy and characterize socially optimal strategy. To determine the optimal queue control policy from a revenue-maximizer perspective, which induces socially optimal behavior and eliminates customer externalities, we propose a joint entrance-fee/abandonment-threshold mechanism. We show that using a pricing policy without abandonment threshold is not sufficient to induce socially optimal behavior and in many cases results in a profit lower than the maximum social welfare the system can generate. Also, considering both customer characteristics and queue control policy, our findings suggest that customers with a moderate anticipation time provide higher expected revenue, acknowledging the importance of understanding customer behavior with respect to both wait time and risk attitude in the presence of anticipation time. In the second model, we consider a two-echelon production inventory system with a single manufacturer and a single distribution center (DC) where the manufacturer has a finite production capacity. There is a positive transportation time between the manufacturer and the DC. Each customer gains a value when receiving the product and suffers a waiting cost when incurring a delay. We assume that customers' waiting cost depends on their degree of impatience with respect to delay (delay sensitivity). We consider a nonlinear waiting cost function to show the degree of risk aversion (impatience intensity) of customers. We assume that customers follow the strategy p where they join the system and place an order with probability p. We analyze the inventory system with a base-stock policy in both the DC and the manufacturer. Since customers and supply chain holder are strategic, we study the Stackelberg equilibrium assuming that the DC acts as a Stackelberg leader and customers are the followers. We first obtain the total expected revenue and then derive the optimal base-stock level as well as the optimal price at the DC.
Static Decision Models For Queueing Systems With Nonlinear Waiting Costs
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Author : Stanford University. Department of Operations Research
language : en
Publisher:
Release Date : 1968
Static Decision Models For Queueing Systems With Nonlinear Waiting Costs written by Stanford University. Department of Operations Research and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Optimal Information Price In Queuing Systems
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Author : Igor Rochlin
language : en
Publisher:
Release Date : 2018
Optimal Information Price In Queuing Systems written by Igor Rochlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Service systems with queues are all around us in our daily life. It is commonly found that in service queuing systems known, the decision whether to join the system made prior to the observation of the queue. If offered the opportunity, customers may rather pay a price for inspecting the queue prior to the decision to join, lowering their chance of encountering a busy queue and spending precious time on waiting. The provider's dilemma is for what price to reveal this information, and whether there is an optimal price which can maximize system's throughput or provider's revenue. The main purpose in this work, is obtaining the optimal pricing mechanism of queue statues prior to the decision to join with general service time distribution. The first step is to formalize the optimization problem. The lack of assumptions regarding the service time distribution makes the analysis complex. This is because, unlike the memoryless case, the information regarding the queue length plays a role in assessing the residual service time. The second step is presenting an example of anumerical solution, which has to depend on the service time distribution. -- abstract.
Price Scheduling In A Time Sharing Queueing System
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Author : J. M. Babad
language : en
Publisher:
Release Date : 1973
Price Scheduling In A Time Sharing Queueing System written by J. M. Babad and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Queuing theory categories.
This thesis deals with a time-sharing system in which users may join after paying an appropriate toll and are subjected to service and waiting charges. The form of an optimal joining policy that minimizes the expected loss of users who may join the system at some of its queues is derived, and is shown to be a control-limit policy with a single control number for every possible entry queue; a newly arriving user will join the minimal-priority entry queue that is not filled up to its contrl number. Tolls and charges that maximize the average expected revenue of the system, as well as the control numbers, are determined for a round-robin time-sharing system. A multi-entrance foreground-background time-sharing system with random entrance is analyzed and the characteristics of the system, such as expected waiting times and expected number of waiting users in each queue, are given. It is shown that when the entry into this system is based on tolls and charges, there exists a set of prices (and associated control numbers) that maximizes the discounted expected revenues of the system.
Assigning Priorities Or Not In Service Systems With Nonlinear Waiting Costs
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Author : Huiyin Ouyang
language : en
Publisher:
Release Date : 2019
Assigning Priorities Or Not In Service Systems With Nonlinear Waiting Costs written by Huiyin Ouyang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
For queueing systems with multiple customer types differing in service time distributions and costs for waiting, it is known that giving priority to one type over others minimizes the long-run average waiting costs when waiting is penalized linearly in time. However, when waiting costs are nonlinear, which is typically a more reasonable depiction of reality, it is not clear whether policies that ignore the type information such as the first-come-first-serve policy (FCFS) should be replaced with type-based priority policies. To shed some light on to this problem, we study a single-server queueing system with two types of customers under static queueing policies that use information on customers' types and order of arrival. Our main theorem ranks the type-based priority policies and FCFS according to their long-run average waiting costs under nonlinear cost functions. We then apply this result to polynomial cost functions and generate insights into when prioritization is advantageous. For example, we find that when customers are similar in terms of their service time distributions, then the parameter region where FCFS is more preferable over type-based priority policies under quadratic costs increases with traffic intensity. We also conduct a numerical study to compare the best static policy with a well-known dynamic policy that requires information on the current waiting times of customers. We find that the best static policy performs comparably with (sometimes even better than) this dynamic policy except when the traffic is heavy and it is not clear which type should receive priority.
Cost Allocation For Queueing Systems With Nonexponential Service Times
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Author : Chun-I. Pedro Lee
language : en
Publisher:
Release Date : 1985
Cost Allocation For Queueing Systems With Nonexponential Service Times written by Chun-I. Pedro Lee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Cost accounting categories.
Modeling And Simulation Concepts
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Author : Rajendra Kumar
language : en
Publisher: Laxmi Publications, Ltd.
Release Date : 2009
Modeling And Simulation Concepts written by Rajendra Kumar and has been published by Laxmi Publications, Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Service Competition With General Queueing Facilities
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Author : Gad Allon
language : en
Publisher:
Release Date : 2011
Service Competition With General Queueing Facilities written by Gad Allon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
In many service industries, companies compete with each other on the basis of the waiting time their customers' experience, along with the price they charge for their service. A firm's waiting time standard may either be defined in terms of the expected value or a given, for instance 95%, percentile of the steady state waiting time distribution. We investigate how a service industry's competitive behavior depends on the characteristics of the service providers' queueing systems. We provide a unifying approach to investigate various standard single stage systems covering the spectrum from M/M/1 to general G/GI/s systems, along with open Jackson networks to represent multi-stage service systems. Assuming that the capacity cost is proportional with the service rates we refer to its dependence on (i) the firm's demand rate and (ii) the waiting time standard as the capacity cost function. We show that across the above road spectrum of queueing models, the capacity cost function belongs to a specific four parameter class of function, either exactly or as a close approximation. We then characterize how this capacity cost function impacts on the equilibrium behavior in the industry. We give separate treatments to the case where the firms compete in terms of (i) prices (only) (ii) their service level or waiting time standard (only), (iii) simultaneously in terms of both prices and service levels. The firms' demand rates are given by a general system of equations of the prices and waiting time standards in the industry.