Simulation and Modelling - Old Questions

1. Define queuing system. Explain different queuing disciplines. Also explain different performance measures for evaluation of queuing system.

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. 

The performance of a queuing system can be evaluated in terms of a number of response parameters, however the following four are generally employed.

• Average number of customer in the queue or in the system
• Average waiting time of the customer in the queue or in the system
• System utilization (Server utilization)
• The cost of waiting time and idle time

1. If  Ta and Ts be the inter arrival time and the mean service time then

• Arrival rate λ=1/Ta 
• Service rate μ=1/Ts
• Average number of customer in the system = λ/(μ - λ)
• Average number of customer in the queue = λ2/μ(μ - λ)
• Average waiting time in the system = 1/(μ - λ)
• Average waiting time in the queue = λ/μ(μ - λ)

2. The ratio of the mean service time to the mean inter arrival time is called traffic intensity. i.e.  u=Ts/Ta

3. Server utilization: It consists of only the arrival that gets served. It is denoted by and defined as

        ρ= λTs= λ/ μ (server utilization for single server).

        ρ= λTs= λ/ nμ (server utilization for n server). 

4. Probability of finding service counter free is (1 – ρ) i.e there are zero customers in the service facility.