Open AccessSynchronized abandonment in discrete-time renewal input queues with vacations
Author(s) -
Veena Goswami,
Gopinath Panda
Publication year - 2022
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.2021163
Subject(s) - queue , computer science , abandonment (legal) , operator (biology) , discrete time and continuous time , observer (physics) , arrival time , time budget , mathematical optimization , real time computing , mathematics , computer network , statistics , biochemistry , chemistry , physics , repressor , quantum mechanics , political science , transcription factor , transport engineering , law , gene , engineering , ecology , biology
We consider a discrete-time infinite buffer renewal input queue with multiple vacations and synchronized abandonment. Waiting customers get impatient during the server's vacation and decide whether to take service or abandon simultaneously at the vacation completion instants. Using the supplementary variable technique and difference operator method, we obtain an explicit expression to find the steady-state system-length distributions at pre-arrival, random, and outside observer's observation epochs. We provide the stochastic decomposition structure for the number of customers and discuss the various performance measures. With the help of numerical experiments, we show that the method formulated in this work is analytically elegant and computationally tractable. The results are appropriate for light-tailed inter-arrival distributions and can also be leveraged to find heavy-tailed inter-arrival distributions.