Service system with non-replenish queue

The paper proposes a probabilistic method for an analysis of service system without input flow, but having initial queue of claims. Such situation takes place in an airport, when an express train delivers passengers from the city. Screening of the arriving passengers is carried out at security checkpoints where a queue of passengers is formed. The queue is not reinforced until the last checked passenger who arrived by train. Considered queueing system has many servers and Erlang distribution of the service time. Formulas are derived for calculating the distribution function of a time until all services ending and the average waiting time. Calculations are supported by the developed MathCAD programs.