Title: Stochastic three-stage hiring model as a tandem queueing process with bulk arrivals and Erlang phase-type selection, M^X/M^(k,K)/1 − M^Y/E_r/1 − ∞

Authors: Aliakbar Montazer Haghighi; Dimitar P. Mishev

Addresses: Department of Mathematics, Prairie View A&M University, P.O. Box 519 MS 2225, Prairie View, Texas, 77446 USA ' Department of Mathematics, Prairie View A&M University, P.O. Box 519 MS 2225, Prairie View, Texas, 77446 USA

Abstract: We consider three possible stages for the handling of job applications in a hiring process as a network queuing model. Applications arrive at the first stage in batches of variable sizes according to Poisson process and are compiled in an 'A-Box'. The batches of variable sizes (within a given minimum and maximum) are processed by a single-processor according to exponential distribution. The accepted portion of each processed batch moves to the second stage, the interview phase, and are piled in an 'I-Box'. The interviews are conducted according to Erlang phase type; each phase according to exponential distribution. The successful applications are, then, directed to the third stage, final hiring phase, and are piled in an 'H-Box'. Using decomposition of the system, we find generation functions and the mean of the number of applications in each of the first two stages. Explicit distributions of the number of applications are found for special cases and numerical examples are also provided.

Keywords: hiring process; network queueing models; stochastic modelling; tandem queueing; bulk arrivals; Erlang phase type; Poisson; exponential; batch sizes; single processor; decomposition; job applications; interviews.

DOI: 10.1504/IJMOR.2013.056100

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.5, pp.571 - 603

Received: 01 Feb 2012
Accepted: 29 Jun 2012
Published online: 31 Mar 2014 *

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