Review Article

Mathematical Analysis of Queue with Phase Service: An Overview

Table 1

Contributions on phase service queueing models using different techniques.

TechniquesAuthors

Probability generating function techniqueRana [73], Murray and Kelton [74], Selvam and Sivasankaran [75], Madan [76, 77], Choi and Kim [78], Madan et al. [79], Griffiths et al. [80], Ke and Chu [81], Kumar and Arumuganathan [82], Salehirad and Badmchizadeh [59], Thangaraj and Vanitha [83], Maurya [84], Kumar et al. [85],
Jain et al. [86], Arivudainambi and Godhandaraman [87]

Supplementary variable techniqueMedhi [88], Madan and Swami [89], Al-Jararha and Madan [90], Madan and Choudhury [91], Madan et al. [79], Madan and Choudhury [92], Jianghua and Jinting [93], Zadeh [94], Wang and Li [95], Ke and Chu. [96], Wang and Li [97], Ramanath and Kalidass [98], Choudhury and Deka [99]

Matrix geometric/matrix methodRamaswami and Lucantoni [100], Le Boudec [101], Diamond and Alfa [102], He and Alfa [103], Breuer et al. [104], Van Houdt et al. [105], Dudin et al. [106], Luh and Xu [107], Lee and Luh [108], Ayyappan et al. [109], Jain et al. [110], Yang et al. [111], Hanbali [112], Jain et al. [113]

Embedded Markov Chain techniqueLatouche and Ramaswami [114], Baburaj and Manoharan [115], Bocharov et al. [116, 117], Atencia et al. [68, 69], Al-khedhairi and Tadj [118], Taramin and Klimenok [119], Jain and Upadhyaya [120], Jain et al. [121]

Maximum entropy analysisJain [122], Wang et al. [123, 124], Singh et al. [125]

Stochastic decomposition property Kim and Park [126], Katayama and Kobayashi [127], Dimitriou and Langaris [128], Park et al. [129], Jain et al. [130, 131]