Open AccessThe impact of the $NT$-policy on the behaviour of a discrete-time queue with general service times
Author(s) -
Bart Feyaerts,
Stijn De Vuyst,
Herwig Bruneel,
Sabine Wittevrongel
Publication year - 2014
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2014.10.131
Subject(s) - queue , computer science , bernoulli's principle , service (business) , independent and identically distributed random variables , discrete time and continuous time , process (computing) , probability generating function , queueing theory , bulk queue , computer network , real time computing , operations research , random variable , mathematics , business , statistics , physics , operating system , marketing , thermodynamics , moment generating function
In this paper, we analyse the behaviour of a discrete-time singleserver queueing system with general service times, equipped with the NTpolicy. This is a threshold policy designed to reduce the number of service unit activation/deactivation cycles, whilst ensuring an acceptable delay trade-off. Once the server is deactivated, reactivation will be postponed until either N customers have accumulated in the queue or the first customer has been in the queue for T slots, whichever happens first. Due to this modus operandi, the system circulates between three phases: empty, accumulating and serving. We assume a Bernoulli arrival process of customers and independent and identically distributed service times. Using a probability generating functions approach, we obtain expressions for the steady-state distributions of the phase sojourn times, the cycle length, the system content and the customer delay. The influence of the threshold parameters N and T on the mean sojourn times and the expected delay is discussed by means of numerical examples