The M / G / s / s Queue

Abstract

This article describes the M / G / s / s queueing system, also known as the Erlang loss model . Customers arrive to this stochastic service system according to a homogeneous Poisson process and request service from one of s parallel servers ( s ≥ 1). The service times are assumed to be independent and identically distributed with a finite mean. Because there is no waiting space in the system, arriving customers who find all s servers busy are lost. Summarized herein are the primary operating characteristics of the M / G / s / s system, namely, the steady‐state probability distribution of the number of occupied servers and the steady‐state blocking probability (the Erlang B formula). Also summarized is the closely related delay probability (the Erlang C formula) for systems with unlimited waiting space. Some computational issues related to the Erlang B and C formulae are also discussed.

The (S−1,S) inventory model and its counterparts in queueing theory

“…The M/G/S/S queue, also called Erlang loss system [7], is a queueing system with Poisson(λ) arrival process, general service time distribution function G(•) with mean τ , S servers and no waiting room. An arriving customer who finds all servers busy is lost.…”

Deploying charging infrastructure for electric vehicles; viability analyses for municipal and private car parking facility operators

“…Based on the expected share of EVs and the strategic demands (the maximum allowable rejection rate because all charging poles are occupied) an M/M/s/s queuing model (Laragan, 2000) (Kharoufeh, 2013) presents a time-dependent deployment strategy for the appropriate charging infrastructure. The number of charging poles, required to satisfy the desired rejection rate, is projected until 2030.…”