Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

There has been a resurgence of interest in demand-responsive shared-ride systems, motivated by concerns for the environment and also new developments in technologies which enable new modes of operations. This paper surveys the research developments on the Dial-A-Ride Problem (DARP) since 2007. We provide a classification of the problem variants and the solution methodologies, and references to benchmark instances. We also present some application areas for the DARP, discuss some future trends and challenges, and indicate some possible directions for future research.

A survey of dial-a-ride problems: Literature review and recent developments

With the rapid development and popularization of mobile and wireless communication technologies, ridesourcing companies have been able to leverage internet-based platforms to operate e-hailing services in many cities around the world. These companies connect passengers and drivers in real time and are disruptively changing the transportation industry. As pioneers in a general sharing economy context, ridesourcing shared transportation platforms consist of a typical two-sided market. On the demand side, passengers are sensitive to the price and quality of the service. On the supply side, drivers, as freelancers, make working decisions flexibly based on their income from the platform and many other factors. Diverse variables and factors in the system are strongly endogenous and interactively dependent. How to design and operate ridesourcing systems is vital—and challenging—for all stakeholders: passengers/users, drivers/service providers, platforms, policy makers, and the general public. In this paper, we propose a general framework to describe ridesourcing systems. This framework can aid understanding of the interactions between endogenous and exogenous variables, their changes in response to platforms’ operational strategies and decisions, multiple system objectives, and market equilibria in a dynamic manner. Under the proposed general framework, we summarize important research problems and the corresponding methodologies that have been and are being developed and implemented to address these problems. We conduct a comprehensive review of the literature on these problems in different areas from diverse perspectives, including (1) demand and pricing, (2) supply and incentives, (3) platform operations, and (4) competition, impacts, and regulations. The proposed framework and the review also suggest many avenues requiring future research.

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=5517&context=sis_research

Ridesourcing systems: A framework and review

Fleet-sizing and service availability for a vehicle rental system via closed queueing networks

Over the last few years, bike-sharing systems have emerged as a new mode of transportation in a large number of big cities worldwide. This new type of mobility mode is still developing, and many challenges associated with its operation are not well addressed yet. One such major challenge of bike-sharing systems is the need to respond to fluctuating demands for bicycles and for vacant lockers at each station, which directly influences the service level provided to its users. This is done using dedicated repositioning vehicles (light trucks) that are routed through the stations, loading and unloading bicycles to/from them. Performing this operation during the night when the demand in the system is negligible is referred to as the static repositioning problem. In this paper, we propose a 3-step mathematical programming based heuristic for the static repositioning problem. In the first step, stations are clustered according to geographic as well as inventory (of bicycles) considerations. In the second step the repositioning vehicles are routed through the clusters while tentative inventory decisions are made for each individual station. Finally, the original repositioning problem is solved with the restriction that traversal of the repositioning vehicles is allowed only between stations that belong to consecutive clusters according to the routes determined in the previous step, or between stations of the same cluster. In the first step the clusters are formed using a specialized saving heuristic. The last two steps are formulated as Mixed Integer Linear Programs and solved by a commercial solver. The method was tested on instances of up to 200 stations and three repositioning vehicles, and was shown to outperform a previous method suggested in the literature for the same problem.

https://www.eng.tau.ac.il/%7Etzur/A%203-step%20heuristic%20-%20TR%20B%20(2015).pdf

A 3-step math heuristic for the static repositioning problem in bike-sharing systems

Operation of on-demand services like taxis, dynamic ridesharing services, or vehicle sharing depends significantly on the positioning of idle vehicles to anticipate future demand and operational states. A new queueing-based formulation is proposed for the problem of relocating idle vehicles in an on-demand mobility service. The approach serves as a decision support tool for future studies in urban transport informatics and design of new types of urban mobility systems like carsharing, ridesharing, and smart taxis. A Lagrangian Decomposition heuristic is developed and compared with a relaxed lower bound solution. Using New York taxicab data, the proposed algorithm reduces the cost by up to 27% compared to the myopic case.

https://rosap.ntl.bts.gov/view/dot/42407/dot_42407_DS1.pdf

Non-myopic relocation of idle mobility-on-demand vehicles as a dynamic location-allocation-queueing problem

Non-myopic dial-a-ride problem and other related dynamic vehicle routing problems often ignore the need for non-myopic pricing under the assumption of elastic demand, which leads to an overestimation of the benefits in level of service and resulting inefficiencies. To correct this problem, a new dynamic dial-a-ride policy is introduced, one that features non-myopic pricing based on optimal tolling of queues to fit with the multi-server queueing approximation method proposed by Hyttia et al. (2012) for large-scale systems. By including social optimal pricing, the social welfare of the resulting system outperforms the marginal pricing assumed for previous approaches over a range of test instances. In the examples tested, improvements in social welfare of the non-myopic pricing over the myopic pricing were in the 20–31% range. For a given demand function, we can derive the optimal fleet size to maximize social welfare. Sensitivity tests to the optimal price confirm that it leads to an optimal social welfare while the marginal pricing policy does not. A comparison of single passenger taxis to shared-taxis shows that system cost may reduce at the expense of decreased social welfare, which agrees with the results of Jung et al. (2013).

A scalable non-myopic dynamic dial-a-ride and pricing problem

A simulated annealing approach for the multi-periodic rail-car fleet sizing problem

As urbanization increases and new business models for transportation and mobility arise, the design of transportation networks should no longer be done in a vacuum. Design interactions between multiple networks have largely been analyzed either as non-cooperative games with non-unique Nash equilibria, even if assumptions needed for such games are not satisfied, or using knowledge-based or agent-based methods that cannot explicitly quantify network sensitivities. A new framework is proposed to model network design in the presence of coexisting networks using multiobjective optimization in a novel manner to identify symbiotic relationships. The framework does not require strict assumptions about availability of information or timing of decisions, and it can be used to examine network sensitivities that knowledge-based methods cannot. A bundled discount pricing problem and subsidy problem are derived from the symbiotic relationships. The framework is applied to formulate a symbiotic bike-sharing network design problem in the presence of a coexisting transit system as a departure-time-elastic multicommodity flow problem. A small network example demonstrates the potential dependency between transit systems and bike-sharing systems for the first time, and the existence of an optimal discount value for considering bundled fares. A larger bike-sharing network, BIXI, is examined in the presence of the Toronto Transit Commission (TTC) in downtown Toronto to address the question of subsidy. It is found that BIXI is operating in a relatively transit-friendly state, and subsidy by TTC to maintain a status quo in Toronto may be worth considering if the cost of subsidy is less than a conservative average reduction achieved of 2.43 units of transit-only user cost for every 1 unit increase of bike-sharing cost.

Hamid R. Sayarshad

Papers

Non-myopic relocation of idle mobility-on-demand vehicles as a dynamic location-allocation-queueing problem

A scalable non-myopic dynamic dial-a-ride and pricing problem

A simulated annealing approach for the multi-periodic rail-car fleet sizing problem

Symbiotic network design strategies in the presence of coexisting transportation networks

Solving a multi periodic stochastic model of the rail–car fleet sizing by two-stage optimization formulation