Mathematical Analysis of Queue with Phase Service: An Overview

Table 4

Literature on unreliable server queue with phase service.

Models	Special features	Authors	Methodology
/M/1	-policy, Vacation, startup, bulk arrival, gated service, and two-phase service	Kumar et al. [85]	Probability generating function
M//1	Erlangian phase service	Yu et al. [146]
M/G/1	Retrial queue, Bernoulli vacation, two-phase service	Wang and Li [147]
	Second optional service	Wang and Xu [148], Choudhury and Tadj [149]
	Startup, second optional service	Wang et al. [150]
	Retrial queue, startup, and two-phase service	Dimitriou and Langaris [151]	Probability generating function, supplementary variable
	Vacation, two-phase essential service	Thangaraj and Vanitha [152], Jain et al. [130, 131]
	Two phase service, Bernoulli vacation	Choudhury and Deka [99]
/G/1	Retrial queue, Bulk arrival, Two phase service	Kumar and Arumuganathan [143], Choudhury et al. [153]
	Bulk arrival, Bernoulli vacation, -policy, and two-phase service	Choudhury and Tadj [154]