Extended Hypercube Models for Large Scale Spatial Queueing Systems

Different than the conventional queueing systems, in spatial queues, servers travel to the customers and provide service on the scene. This property makes them applicable to emergency response (e.g. ambulances, police, fire brigades) and on-demand transportation systems (e.g. shuttle bus services, paratransit, taxis). The difference between the spatial queues and conventional queueing systems is various types of customers and servers and different service rates for different customer-server pairs. For the Markovian arrival and service characteristics, one of the methods to find system performance measures is to model and calculate steady state probability of the Markov chain for the hypercube queueing model (1). One of the obstacles on the way to apply hypercube queueing models to real life problems is the size of the problem; it grows exponentially with the number of servers and a linear system with exponential number of variables should be solved for each instance. In this research, in order to increase scalability of the problem, the authors propose two new models. In addition to that, the authors modeled the problem by using Monte Carlo simulation and tested the convergence and stability properties of the simulation results and compared them with stationary distributions. In the final part, a mixed integer linear programming formulation is given for optimal server configuration with different objectives improving different performance measures. As a future work, the authors are planning to use the optimal solutions of this formulation to evaluate different dispatching policies.

  • Supplemental Notes:
    • This paper was sponsored by TRB committee ADB30 Transportation Network Modeling
  • Corporate Authors:

    Transportation Research Board

    500 Fifth Street, NW
    Washington, DC  United States  20001
  • Authors:
    • Boyaci, Burak
    • Geroliminis, Nikolas
  • Conference:
  • Date: 2012

Language

  • English

Media Info

  • Media Type: Digital/other
  • Features: Figures; References;
  • Pagination: 22p
  • Monograph Title: TRB 91st Annual Meeting Compendium of Papers DVD

Subject/Index Terms

Filing Info

  • Accession Number: 01371504
  • Record Type: Publication
  • Report/Paper Numbers: 12-2010
  • Files: TRIS, TRB
  • Created Date: May 30 2012 3:02PM