16 citations · 35 across the 10 of their papers we have counts for
7 papers · 1 filter
Supermarket Queueing System in the Heavy Traffic Regime. Short Queue Dynamics
Patrick Eschenfeldt, David Gamarnik
We consider a queueing system with parallel queues operating according to the so-called "supermarket model" in which arriving customers join the shortest of randomly select…
Join the Shortest Queue with Many Servers. The Heavy Traffic Asymptotics
Patrick Eschenfeldt, David Gamarnik
We consider queueing systems with n parallel queues under a Join the Shortest Queue (JSQ) policy in the Halfin-Whitt heavy traffic regime. We use the martingale method to prove tha…
Analysis of an M/M/1 Queue Using Fixed Order of Search for Arrivals and Service
Patrick Eschenfeldt, Ben Gross, Nicholas Pippenger
We analyze an M/M/1 queue with a service discipline in which customers, upon arriving when the server is busy, search a sequence of stations for a vacant station at which to wait,…
Stochastic Service Systems, Random Interval Graphs and Search Algorithms
Patrick Eschenfeldt, Ben Gross, Nicholas Pippenger
We consider several stochastic service systems, and study the asymptotic behavior of the moments of various quantities that have application to models for random interval graphs an…
The M/M/Infinity Service System with Ranked Servers in Heavy Traffic
Patrick Eschenfeldt, Ben Gross, Nicholas Pippenger
We consider an M/M/Infinity service system in which an arriving customer is served by the first idle server in an infinite sequence S_1, S_2, ... of servers. We determine the first…
Asymptotic Behavior of the Moments of the Maximum Queue Length During a Busy Period
Patrick Eschenfeldt, Ben Gross, Nicholas Pippenger
We give a simple derivation of the distribution of the maximum L of the length of the queue during a busy period for the M/M/1 queue with lambda<1 the ratio between arrival rate an…