Queuing model of vertical transportation during the down traffic pattern

this paper considers a discrete-time elevator queuing model with general service time distribution and finite waiting space during the down traffic pattern in a two-level warehouse. First we derive the equation of transition probability at floor 2. Based on mathematical software package-MATLAB, we carry out the stationary queue-length distribution just after a service completion with the help of the embedded Markov chain technique. Besides, we explore service time distribution. Furthermore, we establish the relationship between the queue-length distribution just after a service completion and that at a random epoch. With this relationship, we obtain the queue-length distribution at random epoch, from which important performance measures of practical interest, such as the mean queue length are also obtained. Finally some numerical examples are presented. Theoretical results are compared with simulated results, and the validity of the theories is discussed.