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Preprints, Working Papers, ... Year : 2023

Spatial Queues with Nearest Neighbour Shifts

B R Vinay Kumar
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Abstract

Motivated primarily by electric vehicles (EV) queueing at charging stations, in this work we study multiple server queues on a Euclidean space. We consider N servers that are distributed uniformly in [0, 1] d. Customers or EV users arrive at the servers according to Poisson processes of intensity λ. However, they probabilistically decide whether to join the queue they arrived at, or move to one of the nearest neighbours. The strategy followed by the customers affects the load on the servers in the long run. In this paper, we are interested in characterizing the fraction of servers that bear a larger load as compared to when the users do not follow any strategy, i.e., they join the queue they arrive at. These are called overloaded servers. We evaluate the expected fraction of overloaded servers in the system for the one dimensional case (d = 1) when the users follow probabilistic nearest neighbour shift strategies.
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Dates and versions

hal-04201357 , version 1 (09-09-2023)

Identifiers

  • HAL Id : hal-04201357 , version 1

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B R Vinay Kumar. Spatial Queues with Nearest Neighbour Shifts. 2023. ⟨hal-04201357⟩
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