E. Hyytiä, S. Aalto, A. Penttinen and R. Sulonen, A stochastic model for a vehicle in a dial-a-ride system, Operations Research Letters, vol. 38, no. 5, pp. 432-435, Elsevier, 2010.
Abstract: We describe a stochastic model for a system which can serve n customers at the same time, and each accepted and departing customer generates a service interruption. The model describes a single vehicle in a dial-a-ride transportation system in which customers are picked up and dropped individually. Each stop generates an interruption, which corresponds to the deviation from the main route to the pickup/drop location and to the actual stop time. During this time no customer is served or new may arrive. The proposed model is closely related to Erlang's loss system. We give closed form expressions for several important performance quantities: blocking probability, acceptance rate, and the mean sojourn time, which are all shown to be insensitive with respect to the forms of the distributions defining the workload and interruption duration. In other words, similarly as with ordinary Erlang's loss system, the main performance quantities depend only on the mean values.
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BibTeX entry:
@article{hyytia-orl-2010,
author = {Esa Hyyti{\"a} and Samuli Aalto and Aleksi Penttinen and Reijo Sulonen},
title = {A stochastic model for a vehicle in a dial-a-ride system},
journal = {Operations Research Letters},
publisher = {Elsevier},
volume = {38},
number = {5},
doiopt = {10.1016/j.orl.2010.05.009},
year = {2010},
month = {Sep.},
pages = {432--435},
}