Work

Overlap times in the infinite server queue

Year: 2023

Type: article

Abstract: Imagine, you enter a grocery store to buy food. How many people do you overlap with in this store? How much time do you overlap with each person in the store? In this paper, we answer these questions by studying the overlap times between customers in the infinite server queue. We compute in closed form the steady-state distribution of the overlap time between a pair of customers and the distribution of the number of customers that an arriving customer will overlap with. Finally, we define a residual process that counts the number of overlapping customers that overlap in the queue for at least $\delta$ time units and compute its distribution.

Source: Probability in the Engineering and Informational Sciences

DOI: 10.1017/s0269964822000456

Authors: Sergio Palomo, Jamol Pender

Institution: Cornell University

Language: English

Topic: Advanced Queuing Theory Analysis

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,255

Funders: National Science Foundation, Alfred P. Sloan Foundation, Division of Mathematical Sciences