Waiting Line Theroy BY, PRAYASH NEUPANE, KARAN CHAND & SANTOSH SHERESTHA

What is queuing ??  Queues or waiting lines arise when the demand for a service facility exceeds the capacity of that facility, that is, the customers do not get service immediately upon request but must wait, or the service facilities stand idle and wait for customers.  Waiting lines, or queues are a common occurrence both in everyday life and in variety of business and industrial situations.  For example: Banks must decide how many teller windows to keep open to serve customers during various hours of the day.  Manufacturing plants must determine the optimal number of mechanics to have on duty in each shift to repair machines that break down.  Supermarkets must decide how many cash register check out positions should be opened.

BASIC COMPONENTS OF A QUEUING SYSTEM  INPUT SOURCE OF QUEUE An input source is characterized by  Size of the calling population: Arrival at a service may be drawn from a finite or an infinite population.  Pattern of arrivals at the system: The arrivals pattern of customer to the service system is either static or dynamic.  Behavior of the arrivals: The arriving customer shows different kind of behaviors that may be patient or impatient.

Queue Discipline  A queue discipline is a priority rule or set of rules for determining the order of service to customers in a waiting line.  The rules selected can have dramatic effect on the system’s overall performance  No. of customer in line, the average waiting time, range of variability in waiting time and the efficiency of the service facility are few factors affected by the choice of priority rule.

Major Queue Discipline  First-come, first served: Consumer are served in the order of their arrival.  Last-come, first served: Customer or unit coming last are served first.  Service in random order: Customer are selected for random irrespective of their arrivals.  Priority Service: Customer are grouped in priority classes on the basis of some attributes such as service urgency, and FCFS rule is used within each class to provide service.  Pre-emptive priority: The highest priority customer is allowed to enter into the service immediately after into the system even if a customer with lower priority is already in service.  Non-pre-emptive priority: Highest priority customer goes ahead in the queue, but service is started immediately on completion of current service.

Service Process  The service process is concern with the manner in which customers are serviced and leave the service system. It is characterized by: Arrangement and capacity of service facility and Distribution of service time.  Arrangement and capacity of service facility: The capacity of service mechanism is measured in terms of customers that can be served simultaneously and effectively on unit time. Eg, hour, day etc. It may have different layout such as series arrangements, parallel arrangements and mixed arrangements.  Series arrangements: Series arrangement consists of a sequence of a number of service facilities such that a customer must go through one facility after another in a particular sequence before the whole service. It can be single queue, single server or single queue, multiple servers. Eg, during college admissions, the student go through one counter after another before their admission formalities is completed.

conted  Parallel arrangements: The service facilities are arranged in parallel to each other. This provides opportunity for customer to join any service central of his choice. Check in point of airport is best example.  Mixed arrangements: Consists of service facilities in both series as well as parallel form. This type of arrangements are often seen in hospitals or universities.  Distribution of service time: The time interval from the commencement of service to the completion of service for a customer is known as service time. The capacity of servers in number of units per time period is called service rate. The service time distribution can be described in terms of either Poisson or as exponential distribution.

Types of Waiting Line System  Single channel system  Multi channel system  Single queue with many service counter system  Many queue with single counter system  Multi stage system

Single channel system Single Server – Single Queue  The models that involve one queue – one service station facility are called single server models where customer waits till the service point is ready to take him for servicing. Students arriving at a library counter is an example of a single server facility.

Single Server – Several Queues  In this type of facility there are several queues and the customer may join any one of these but there is only one service channel.

Several (Parallel) Servers – Single Queue  In this type of model there is more than one server and each server provides the same type of facility. The customers wait in a single queue until one of the service channels is ready to take them in for servicing.

Multi channel System Several Servers – Several Queues  This type of model consists of several servers where each of the servers has a different queue. Different cash counters in an electricity office where the customers can make payment in respect of their electricity bills provide an example of this type of model.

Multi Stage Channel  A service center opens different counter for providing services in sequence and customer are asked to pass through required counters for getting respective service.

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