Extended Hypercube Models for Large Scale Spatial Queueing Systems

Boyacı, Burak and Geroliminis, Nikolas (2011) Extended Hypercube Models for Large Scale Spatial Queueing Systems. In: STRC 2011 - 11th Swiss Transport Research Conference, 2011-05-11 - 2011-05-13.

Text (boyaci2011STRC)
boyaci2011STRC.pdf - Accepted Version
Download (2MB)

Abstract

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 systems (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 (HQM) (Larson, 1974). One of the obstacles on the way to apply HQMs 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, we propose two new models. In addition to that, we modeled the problem by using Monte Carlo simulation and tested the convergence and stability properties of the simulation results and compare them with stationary distributions.