Endogenous arrivals in batch queues with constant or variable capacity

We study batch queueing systems with continuous time, finite commuter populations, single server, and endogenously determined arrival times. Symmetric equilibrium solutions in mixed strategies are constructed and subsequently tested in two experiments that examine two different batch queueing models, one with a fixed server capacity, and the other with a variable server capacity. With experience in playing the stage queueing game repeatedly, experimental results from groups of 20 subjects support equilibrium play on the aggregate level when the server capacity is fixed and commonly known. When it is known to be variable, randomly changing from round to round, subjects diverge from equilibrium play and increase their individual payoffs substantially by significantly shortening their waiting time.

[1]  M. Neuts A General Class of Bulk Queues with Poisson Input , 1967 .

[2]  Amnon Rapoport,et al.  Joining a Queue or Staying Out: Effects of Information Structure and Service Time on Arrival and Staying Out Decisions , 2005 .

[3]  André de Palma,et al.  OPTIMAL TIMETABLES FOR PUBLIC TRANSPORTATION , 2001 .

[4]  Amnon Rapoport,et al.  Departure Times in Y-Shaped Traffic Networks with Multiple Bottlenecks , 2009 .

[5]  Shelley E. Taylor,et al.  Heuristics and Biases: When Predictions Fail: The Dilemma of Unrealistic Optimism , 2002 .

[6]  Amnon Rapoport,et al.  Equilibrium Play in Single-Server Queues with Endogenously Determined Arrival Times , 2004 .

[7]  Hai Yang,et al.  Equilibrium properties of the morning peak-period commuting in a many-to-one mass transit system , 2007 .

[8]  Norman T. J. Bailey,et al.  On Queueing Processes with Bulk Service , 1954 .

[9]  Howard J. Weiss The Computation of Optimal Control Limits for a Queue with Batch Services , 1979 .

[10]  Amit Pazgal,et al.  Comparison of customer balking and reneging behavior to queueing theory predictions: An experimental study , 2008, Comput. Oper. Res..

[11]  D. Dunning,et al.  Ambiguity and self-evaluation: the role of idiosyncratic trait definitions in self-serving assessments of ability , 1989 .

[12]  W. Vickrey Congestion Theory and Transport Investment , 1969 .

[13]  M. L. Chaudhry,et al.  A first course in bulk queues , 1983 .

[14]  D. Kahneman,et al.  Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias , 1991 .

[15]  Charles A. Holt,et al.  Waiting-Line Auctions , 1982, Journal of Political Economy.

[16]  Anthony Barnett On operating a shuttle service , 1973, Networks.

[17]  J. A. Sniezek,et al.  Passion, Preference, and Predictability in Judgmental Forecasting , 1992 .

[18]  Refael Hassin,et al.  To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems , 2002 .

[19]  D. Kahneman,et al.  Heuristics and Biases: The Psychology of Intuitive Judgment , 2002 .

[20]  Amnon Rapoport,et al.  Batch Queues with Choice of Arrivals: Equilibrium Analysis and Experimental Study , 2004 .

[21]  A. Palma,et al.  SCHEDULE DELAY AND DEPARTURE TIME DECISIONS WITH HETEROGENEOUS COMMUTERS , 1988 .

[22]  M. J. Phillips,et al.  Stochastic theory of service systems , 1974 .

[23]  A. Palma,et al.  A STRUCTURAL MODEL OF PEAK-PERIOD CONGESTION: A TRAFFIC BOTTLENECK WITH ELASTIC DEMAND. IN: RECENT DEVELOPMENTS IN TRANSPORT ECONOMICS , 1993 .

[24]  Colin Camerer Behavioral Game Theory , 1990 .

[25]  J. Kagel,et al.  Handbook of Experimental Economics , 1997 .

[26]  Marvin Kraus,et al.  A new look at the two-mode problem , 2003 .

[27]  Howard J. Weiss Technical Note - Further Results on an Infinite Capacity Shuttle with Control at a Single Terminal , 1981, Oper. Res..

[28]  J. Medhi,et al.  Waiting Time Distribution in a Poisson Queue with a General Bulk Service Rule , 1975 .

[29]  F. W. Irwin,et al.  Stated expectations as functions of probability and desirability of outcomes. , 1953, Journal of personality.

[30]  Refael Hassin,et al.  Equilibrium Arrivals in Queues with Bulk Service at Scheduled Times , 1987, Transp. Sci..

[31]  P. Naor The Regulation of Queue Size by Levying Tolls , 1969 .

[32]  Yuichiro Yoshida,et al.  The Commuter's Time-of-Use Decision and Optimal Pricing and Service in Urban Mass Transit , 2002 .

[33]  Marc Willinger,et al.  Road Traffic Congestion and Public Information: An Experimental Investigation , 2006 .