Simulation and Modelling - Old Questions

10.  What do you understand by queueing and queueing discipline? An office works for 5 days, 8 hours per day, and receives 1200 telephone call in the week. Calculate the mean arrival rate and mean inter-arrival time of the calls.

The line where the entities or customer wait is generally known as queue. The combination of all entities in system being served and being waiting for service will be called as queueing system.

Queue discipline refers to the rule that a server uses to choose the next customer from the queue when the server completes the service of the current customer. Common queue disciplines include first-in-first-out (FIFO); last-in-first-out (LIFO); service in random order (SIRO); shortest processing time first (SPT); and service according to priority (PR).

• First in first out :This principle states that customers are served one at a time and that the customer that has been waiting the longest is served first.
• Last in first out : This principle also serves customers one at a time, however the customer with the shortest waiting time will be served first. 
• Service in random order: A customer is picked up randomly from the waiting queue for service.
• Shortest job first: The next job to be served is the one with the smallest size (shortest service time).
• Priority: Customers with high priority are served first.

Now,

Mean arrival rate = λ

Mean inter-arrival time = T_a

Total working hours = 5 * 8 = 40 hrs per week

Total calls in the week = 1200

T_a  =  (40*60*60 sec)/1200 = 144,000 sec/1200 = 120 sec = 2 min

λ = 1/T_a = 1/2 = 0.5 call per min