The editor has retracted this article because the article shows significant overlap with two other publications by R. Sudhesh and A. Azhagappan without proper citation [1, 2]. A. Azhagappan does not agree to this retraction. The online version of this article contains the full text of the retracted article as electronic supplementary material.

  1. [1

    ] Sudhesh R, Azhagappan A. Transient Analysis of M/M/1 Queue with Server Vacation Customers Impatient and a Waiting Server Timer. Asian Journal of Research in Social Sciences and Humanities. 2016;6(9):1096–104.

  2. [2

    ] Sudhesh R, Azhagappan A. Transient analysis of an M/M/1 queue with variant impatient behavior and working vacations. OPSEARCH. 2018 Nov 1;55(3-4):787–806.