Mathematical Analysis of Queue with Phase Service: An Overview

Table 3

Literature on vacation queue with phase service.

Models	Special features	Authors	Methodology
M/M/1	Second optional service in batches	Jain et al. [86]	Probability generating function
	Retrial queue, Bernoulli vacation, and two-phase service	Choudhury [134]	Embedded Markov chain, probability generating function
		Choudhury and Kalita [140]	Probability generating function
M/G/1	Bernoulli vacation, server breakdown, and two-phase service	Ke and Chang [141]
	Bulk arrival, multiple vacation	Jeyakumar and Arumuganathan [142]
	Retrial queue, server breakdown, batch arrival, and two-phase service	Kumar and Arumuganathan [143]
	Multioptional services, multi-optional vacations, and unreliable server	Jain et al. [72]	Probability generating function, supplementary variable technique
/(G1, G2)/1	Bulk arrival, setup, bilevel threshold policy, single vacation, and two phases of essential service	Mary et al. [144]	Probability generating function, supplementary variable technique, and stochastic decomposition
BMAP/G/1	Bulk arrival, multiple vacations, and second optional service	Wu et al. [145]	Probability generating function