A Birth–Death Queueing Model for Optimal Threshold Recruitment in Manpower Organizations

This study develops two queuing manpower models, QMPM-1 and QMPM-2, where the manpower sequence evolves on a finite state space as a birth–death process governed by a threshold-recruitment level ‘L’. Random attrition follows a Poisson process with a positive mean rate. However, beyond the level L, the attrition rate rises depending on the sensitivity to workforce overload that comes from congestion. Inter-recruitment times follow an exponential law with an average positive rate. In QMPM–1, recruitment is stopped when the workforce exceeds L, while in QMPM–2, a reduced but strictly positive recruitment rate is maintained even in the overloaded region. The study obtains both transient and stationary solutions and verifies the stability of QMPM-1 using a Foster–Lyapunov drift criterion. A long-run cost function involving staffing, recruitment, and congestion penalties is formulated to determine the optimal threshold. Numerical illustrations support that weak recruitment compared to attrition ratio results in low optimal thresholds, while the stronger recruitment effectiveness allows for higher thresholds that can favor larger and more stable workforce levels.