Performance Evaluation 80 (2014) 1–4
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Preface
Special Issue of Performance Evaluation on Service Science of Queues with Human Servers
Over the recent decades, a great advancement in the theory of queues has been driven by its ingenious applications to the performance evaluation of computer systems and communication networks. Conversely, such theoretical treatment contributed significantly to the development of these technologies which have brought today’s prosperity of informationbased society. Since its commencement in 1981, the Performance Evaluation journal has played key roles by providing a number of theoretical breakthroughs in this interplay of theories and technologies. However, the use of analytic studies is now becoming less evident in these fields. I think there are two reasons for this decline. First, queueing theory, which used to be in the center of analytical methods, has lost its place to make impacts. Generally speaking, queues arise when resources are scarce compared to demands. Nowadays, hardware resources are no longer scarce in most systems of computer and communication. The rapid technological development, often referred to as Moore’s law, has brought powerful CPU and abundant memory for computers as well as virtually unlimited bandwidth of optical fiber for telecommunication networks so cheaply that we do not have to concern ourselves with the sophisticated use of these resources. (An exception may be the wireless communication where the available spectrum of radio frequency continues to be a physically limited resource.) Second, the protocol and control of the operation in these systems have become so complicated and interdependent that the theoretical treatment, often based on simplifying fictitious assumptions such as independence of events and exponential (phase-type at most) distributions, cannot cope with the operation of real systems. Thus it is no wonder that analytic methods individually contrived by the human brain power have been replaced by algorithmic and event-driven simulation methods which can make stepwise steady progress on top of the ever-growing computer power. In the meantime, the service sector of industry now takes a predominant portion of the national economy in terms of gross domestic product (GDP) as well as the population share of labor force not only in advanced countries but also in developing countries. Unlike manufacturing, however, not much scientific approach has been exploited so far for the increase of productivity and promotion of innovation in the service industry. It is just 10 years ago that the services science was advocated as a new academic discipline in the so-called Palmisano Report from the Council on Competitiveness in the United States [1]. Since then, many national projects as well as academic and industrial initiatives have followed suit. In opposition to engineering systems, resources are scarce in service systems in which human beings are involved as customers and servers such as hospitals (patients as customers, doctors and nurses are servers), call centers (human customers and operators), and theme parks (guests make a huge queue for the Space Mountain). As a matter of fact, representative textbooks on service management and service marketing [3,5,9] discuss inevitable waiting lines in everyday life in their chapters on resource management. According to these books, the value of service is co-created by customers and servers. Thus we must consider not only customer satisfaction but also server satisfaction, the latter of which we did not care in computer and communication systems. Human beings remain to be precious resources for value creation that may not be abused in human service systems. According to my view, the study of service systems with human customers and servers is one of a few fields in which the queueing theory can still make prominent impacts on the practical side. Application of queueing theory to human service systems is not new at all. It was only that its exclusively driving application was computers and communication networks from the early 1960s to the 1980s. Science of services is the worthy field of study in the 21st century on the basis of operations research, data science and computer science. Currently, however, only a few books address the queueing theory of intermediate level for service systems [2,4,8]. In the latter half of the 20th century, the queueing theory was vigorously applied to the performance evaluation of computers, communication networks, and manufacturing systems, where the ‘‘customers’’ were jobs, messages, and goods http://dx.doi.org/10.1016/j.peva.2014.07.022 0166-5316/© 2014 Published by Elsevier B.V.
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Preface / Performance Evaluation 80 (2014) 1–4
while the ‘‘servers’’ were CPUs, communication lines, and machineries, respectively. These servers can work 24 hours a day and 7 days a week without fatigue. At that time the goal of system design was to shorten the processing time by maximizing the efficiency with optimal scheduling of precious service resources. In the 21st century when we aim at the application of queueing theory to service systems with human customers and human servers, we must consider the perception of customers when they are waiting before and after receiving the service. Waiting customers are concerned not only with the real waiting time but also with the fairness about their treatment, comfort in the waiting room, and something useful to do while waiting [6]. We must also care about the factors influencing the satisfaction of servers such as fair and balanced job assignment in the staff scheduling. This observation comes from the result of empirical research that there is no customer satisfaction without employee satisfaction in human service systems. Finally, the manager and owner of the system, even the neighborhood of service organization must be satisfied too for the sustainable service business in the community. Below let me discuss several features of queueing models for human service systems that challenge the new generation of queueing theorists [7]. Some of them are already addressed in the papers contained in this special issue.
• Many servers Clearly there is economy of scale in the service system with a single big server. An example is the centralized job processing in a company in the 1970s. A ‘‘main-frame computer’’ was installed in a computer room to process all jobs from the entire company. Another example is a ‘‘broadband communication network’’ in the 1980s where many copper cables were multiplexed into a single optical fiber cable for heavy-duty intercity connection. However, the super highspeed service is neither possible with human servers nor liked by human customers. Thus a human service system usually provides a service facility with many servers of mediocre capability. This configuration actually brings arriving customers less probability of wait and less waiting time than those a system with a single big server does, because each arriving customer waits only if all servers are busy. This fact can be proved exactly for M /M /m queues but such analysis is unavailable for M /G/m queues.
• Time-varying customer arrival rate The amount of service demand from human customers naturally depends on the time of the day according to people’s private and working activities during a day. For example, the customer arrival rate at a restaurant has peaks at meal times. There are few customers around midnight in a supermarket with 24 hour opening. If servers are human, the personnel expenses are proportional to the duration of working hours. Thus the manager tries to control the number of workers depending on the time of day. There are studies of queues with time-varying customer arrival rate and time-varying number of servers, for example, by means of fluid approximation. At this moment, however, the theory does not seem to have developed enough to be easily amenable to practical use.
• Satisfaction of customers and servers If servers are CPUs and communication lines, we do not care about the ‘‘satisfaction’’ of such physical devices. The time scale of their metal fatigue and failure (days, say) is order of magnitude different from the time scale of their operation (less than microseconds, say) so that failure and operation should be treated by different models. However, the dissatisfaction of employees directly affects the quality of service in the same time scale. Also, employees may feel happy and enhance the quality of service immediately after the appreciation from their customers. Therefore, it is essential to consider the satisfaction of customers and servers together that depend on each other simultaneously. In the traditional application of queueing theory, customer satisfaction was discussed in the context of fair resource sharing. But the factors for server satisfaction such as fair and balanced staff scheduling and customer assignment remain to be investigated quantitatively for the engineering of human service systems.
• Workforce management A sad reality is that researchers of queueing theory, those of mathematical optimization, and those of statistics and data science are different species of people who do not talk much to each other. The academic performance of a researcher is evaluated by the publication of papers in journals with high citation indices within their own fields of specialty. However, for the success of scientific approach to service systems, researchers of various specialties must collaborate on the focused problems with their respective contributions. An example is the workforce management for human service systems such as call centers and hospitals. First, data scientists should analyze the time records of customer arrivals and service processes. Then queueing theorists calculate the necessary and sufficient number of employees to meet the satisfaction of customers. Operations researchers provide the optimal staff scheduling to meet the personal requests of employees. Industrial psychologists may be called in for the assessment of work-and-family balance in the resultant work shifts of employees. Only such packaged solution would be accepted by the managers and employees of service systems. With these concerns and perspectives in mind, I called for papers to the special issue of Performance Evaluation on ‘‘service science of queues with human servers’’ in which human aspects of service systems are supposed to be addressed from innovative viewpoints of queueing theory. This issue includes six papers of original studies each with a list of affluent references to the preceding work. Although all papers refer more or less to the application of theories to real service systems, they may be classified into two categories as follows.
Preface / Performance Evaluation 80 (2014) 1–4
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• Application-oriented papers: In the paper ‘‘Designing cyclic appointment schedules for outpatient clinics with scheduled and unscheduled patient arrivals,’’ N. Kortbeek et al. present a method to design the appointment systems for outpatient clinics that offer both walk-in and appointment services when there are scheduled and unscheduled arrivals of patients. Their method tries to maximize the number of unscheduled patients served on the day of arrival while satisfying a prespecified access time norm for scheduled patients. Results of numerical experiments and case studies are shown in detail. In the paper ‘‘Performability evaluation of emergency call center,’’ M.A. de Q.V. Lima et al. provide a theoretical model for evaluating the performance and availability of an actual emergency call center which is composed of energy structure for power supply, network structure for connection to the internet, voice structure for connection to the public telephone network, and customer service structures where calls are queued and handled by agents. The reliability block model and stochastic Petri nets are used for the evaluation of performability for the whole center. The numerical results of the case study are presented in detail. In the paper ‘‘Performance analysis of call centers with abandonment, retrial and after-call work,’’ T. Phung-Duc and K. Kawanishi consider a multiserver queueing model of a call center that has customers’ abandonment and retrials and operators’ after-call work. Performance measures such as the call blocking probability and the distribution of the waiting time (excluding the time that a retrial customer spends in the orbit) are numerically calculated from the rigorous formulation of a continuous-time, level-dependent quasi-birth-and-death process. • Methodology-oriented papers: In the paper ‘‘Optimal capacity management and planning in services delivery centers,’’ A.R. Heching and M.S. Squillante develop a two-phase stochastic optimization solution approach for the capacity management and planning problems in generic human service delivery systems. The two phases consist of the first phase for the stochastic analysis and optimization and the second phase for the simulation-based optimization. The latter exploits the first-phase results as a starting point and captures the complicated characteristics of real-world service delivery systems. Results of numerical experiments and case studies are presented from real-world systems. In the paper ‘‘Approximate blocking probabilities in loss models with independence and distribution assumptions relaxed,’’ A.A. Ali and W. Whitt study the approximations for the blocking probability in stochastic loss models that could be used in hospital-related systems and revenue management of reusable resources. Specifically, they address the non-exponential distributions, dependence between successive interarrival times, and dependence between successive service times in the stationary G/G/s/0 loss model by exploiting the heavy-traffic approximation formulas. The effectiveness of their method is validated by simulation. In the paper, ‘‘G-RAND: A phase-type approximation for the nonstationary G(t )/G(t )/s(t ) + G(t ) queue, S. Creemers et al. aim to handle human service systems that have fluctuations in the intensity of parameters over the day such as the time-varying hourly arrival rate at the emergency department of a hospital. To do so, they present a method to calculate the performance measures by approximating the general interarrival, service, and abandonment time distributions by phase-type distributions and observing the system state at discrete moments in time as a Markov process. When the number of servers decreases below the number of customers in service, both servers and customers are removed together from the system. The accuracy of this method is assessed by simulation study. We are only at the starting point of developing the theories to be applicable for real human service systems. The set of mathematical techniques shown in this special issue is not sufficient to cover all the aspects of human service systems, but I believe that it has paved the way for a new horizon of research. I am very grateful to the authors of these papers who have contributed their original pieces of work, prepared the manuscripts patiently in response to my request for increasing the readability, and have waited a long time until the final publication since the initial submission.
References [1] Council on Competitiveness, Innovate America: Thriving in a World of Challenges and Change, National Innovation Initiative Summit and Report, May 2005. http://www.innovationtaskforce.org/docs/NII%20Innovate%20America.pdf (access: 6/30/2014). [2] M.S. Daskin, Service Science, John Wiley & Sons, 2010. [3] J.A. Fitzsimmons, M.J. Fitzsimmons, Service Management: Operations, Strategy, Information Technology, sixth ed., McGraw-Hill, 2008. [4] R.W. Hall, Queueing Methods: For Services and Manufacturing, Prentice-Hall, 1991. [5] C. Lovelock, J. Wirtz, Services Marketing: People, Technology, Strategy, seventh ed., Prentice-Hall, 2011. [6] D.H. Maister, The psychology of waiting, in: J.A. Czepiel, M.R. Solomon, C.F. Suprenant (Eds.), The Service Encounter, D.C. Heath & Company, 1985, pp. 113–123. [7] H. Takagi, From computer science to service science: Queues with human customers and servers, in: Computer Networks, Vol. 66: Leonard Kleinrock Tribute Issue: A Collection of Papers by his Students, June 2014, pp. 102–111. [8] H. Takagi (Ed.), Introduction to Service Science: Innovation by Mathematical Modeling and Data Analysis, University of Tsukuba Press, August 2014 (in Japanese). [9] V.A. Zeithaml, M.J. Bitner, D.D. Gremler, Service Marketing: Integrating Customer Focus Across the Firm, sixth ed., McGraw-Hill Irwin, 2013.
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Hideaki Takagi is currently Provost and Executive Officer at the University of Tsukuba, Japan. He received his B.S. and M.S. degrees in Physics from the University of Tokyo in 1972 and 1974, respectively. In 1974 he joined IBM Japan as a Systems Engineer. From 1979 to 1983, he studied at the University of California, Los Angeles, and received his Ph.D. degree in Computer Science. From 1983 to 1993, he was with IBM Research, Tokyo Research Laboratory. He moved to the University of Tsukuba in October 1993 as Professor at the Institute of Policy and Planning Sciences. He was Vice President of the University of Tsukuba in 2002–2003. His research interests include queueing theory and stochastic processes as applied to the performance evaluation of computer communication networks and human service systems. He is the author of research monographs Analysis of Polling Systems (MIT Press, 1986), and Queueing Analysis: A Foundation of Performance Evaluation, Volumes 1–3 (Elsevier, 1991–1993). He is the coeditor of Spectrum Requirement Planning in Wireless Communications: Model and Methodology for IMT-Advanced (Wiley, 2008) and the editor of Introduction to Service Science: Innovation by Mathematical Modeling and Data Analysis (University of Tsukuba Press, 2014, in Japanese). He is IEEE Fellow (1996) and IFIP Silver Core Holder (2001). He served as editor for IEEE Transactions on Communications (1986–1993), IEEE/ACM Transactions on Networking (1992–1994), Queueing Systems (1988–2009), and Performance Evaluation (from 1984 onwards).
Hideaki Takagi Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba Science City, Ibaraki 305-8573, Japan E-mail address:
[email protected].