Simulation and modeling - Old Questions

2.  Define the queuing system. Explain the elements of queuing system with example.

10 marks | Asked in 2068

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.

Characteristics/Elements of Queueing System

The key elements of queuing systems are customer and server. Customer refers to anything that arrives at a facility and requires service. E.g. people, machines, trucks, emails. Servers refers to any resource that provides the requested service. E.g. receptionist, tellor, CPU, washing machine etc.

1. Calling Population

The population of potential customers those require service from system is called calling population. It may be finite or infinite. System having large calling population is usually considered as infinite. For e.g. customers at banks, restaurant. And System having less and countable population is usually considered as finite. For e.g. a certain number of machines to be repaired by a service man.

    In finite population model, arrival rate depends on the number of customers being served and waiting. But in infinite population model, arrival rate is not affected by the number of customer being served and waiting.

2. Arrival Process

The arrival process for infinite-population models is usually characterized in terms of interarrival times of successive customers. Arrivals may occur at scheduled times or at random times. When at random times, the inter arrival times are usually characterized by a probability distribution and most important model for random arrival is the poisson process. In schedule arrival interarrival time of customers are constant.

3. Service Process

Service process can be measured by the number of customers served per some unit of time or the time taken to complete the service. Once entities have entered to the system they must be served. The service can be provided in single or batch. if it is batch, as in the case of arrival the batch size can be fixed or random. Service time may be of constant duration or of random duration.

Markov Service process: A Markov service process is a special service process in which entities are processed one at a time in FCFS order and service times are independent and exponential. Aswith the case of Markov arrivals, a Markov service process is memoryless, which means that the expected time until an entity is finished remains constant regardless of how long it has been in service.

4. Queueing Discipline and Queueing Behaviour

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. 

Queue behavior refers to the actions of customers while in a queue waiting for service to begin. Different queue behaviours are:

  • Balk/Balking: It means leaving the queue when the customer see the line is too long.
  • Renege/Reneging: Leave after being in the line when they see that the line is moving too slowly.
  • Jockey/Jockeying: Move from one to a shortest line. 

5. Number of Servers: 

Servers represent the entity that provides service to the customer. A system may consist of single server or multiple servers.
- A system with multiple servers is able to provide parallel services to the customers.