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In the present fast-paced and globalized age of war, special operations forces have a comparative advantage over conventional forces because of their small, highly-skilled units. Largely because of these characteristics, special operations forces spend a disproportionate amount of time deployed. The amount of time spent deployed affects service member’s quality of life and their level of preparedness for the full spectrum of military operations. In this paper, the authors ask the following question: How many force packages are required to sustain a deployed force package, while maintaining predetermined combat-readiness and quality-of-life standards?

The authors begin by developing standardized deployment-to-dwell metrics to assess the effects of deployments on service members’ quality of life and combat readiness. Next, they model deployment cycles using continuous time Markov chains and derive closed-form equations that relate the amount of time spent deployed versus at home station, rotation length, transition time and the total force size.

The expressions yield the total force size required to sustain a deployed capability.

Finally, the authors apply the method to the US Air Force Special Operations Command. This research has important implications for the force-structure logistics of any military force.

This paper evaluates an alternative queuing concept for marine container terminals that utilize a truck appointment system (TAS). Instead of having all lanes providing service to trucks with appointments, this study considers the case where walk-in lanes are provided to serve those trucks with no appointments or trucks with appointments but arrived late due to traffic congestion.

To enable the analysis of the proposed alternative queuing strategy, the queuing system is shown mathematically to be stationary. Due to the complexity of the model, a discrete event simulation (DES) model is used to obtain the average waiting number of trucks per lane for both types of service lanes: TAS-lanes and walk-in lanes.

The numerical experiment results indicated that the considered queuing strategy is most beneficial when the utilization of the TAS lanes is expected to be much higher than that of the walk-in lanes.

The novelty of this study is that it examines the scenario where trucks with appointments switch to the walk-in lanes upon arrival if the TAS-lane server is occupied and the walk-in lane server is not occupied. This queuing strategy/policy could reduce the average waiting time of trucks at marine container terminals. Approximation equations are provided to assist practitioners calculate the average truck queue length and the average truck queuing time for this type of queuing system.