Mathematical Analysis of Queue with Phase Service: An Overview

Table 2

Literature on retrial queue with phase service.

Models	Special features	Authors	Methodology
M/M/1	Vacation interruptions, Erlang- type service	Ayyappan et al. [132]	Matrix geometric technique
M//1	Second optional service	Sekar et al. [133]	Probability generating function
M/G/1	Bernoulli vacation, stochastic decomposition, and two-phase service	Choudhury [134]	Embedded Markov chain, probability generating function
	Server breakdown, SOS	Choudhury and Deka [135]	Probability generating function
	Generalized retrial time, SOS	Choudhury [136]
	() types of retrial customers, -phases of service	Langaris and Dimitriou [137]
/G/1	Bulk arrival, vacation, unreliable server, and two-phase service	Ke and Chang [138]	Probability generating function, supplementary variable
/(G1, G2)/1	Bulk arrival, Bernoulli feedback, optional vacations, and two phases of heterogeneous service	Arivudainambi and Godhandaraman [87]	Probability generating function, supplementary variable technique
BMAP/PH/N	Batch Arrival, server breakdown, -policy, and phase type service	Kim et al. [139]	Probability generating function