The mode for ships queuing is the key to establish a fine handling queuing system, making the operation of
handling queuing system smoothly. According to the characteristics of handling in the ports and ships as well as a
great amounts of statistics data and study abroad, it can be shown that, in most queuing systems for handling service
,the arrival of the ships obeys the Poisson distribution while the time for handling service obeys the negative
exponential distribution.
There are a variety of queuing modes for ships to enter the ports. Then through a port handling example, compare
M/M/1 to M/M/s two kinds of queuing modes. For an instance, there is a port somewhere, with 3 handling servers.
The average ratio for the arrival of ships is λ=0.9 per hour, while the average ratio for service is μ=0.5 per hour. The
arrival process for ships obeys the Poisson distribution while the time for handling service obeys the negative
exponential distribution. After entering the port, the ships will join the queue to wait for accepting the handling
service.
(1) There would be 3 queues if the ships join into the each queue before 3 servers separately after the arrival. The
arrival ratio for each the queue is 0.9 / 3 0.3 1 2 3 λ = λ = λ = = , and this moment, the system is 3 subsystems of
M/M/1.
(2) If the ships join into a queue after the arrival and berth before the free server for handling, and this moment,
the system is a system of M/M/3.
To calculate the efficiency indicators under the conditions of both the queuing modes above respectively, it can be
listed as following table shows.