This document summarizes key concepts about waiting line models:
1. Waiting line models use queueing theory to help managers understand and make decisions about operating characteristics of waiting lines like average wait times and number of customers in the system.
2. Common characteristics of waiting line systems include single channel lines, random and independent customer arrivals modeled by the Poisson distribution, and exponentially distributed service times.
3. The document outlines formulas for calculating operating characteristics of single and multiple channel models based on arrival and service rates when arrivals follow Poisson and service times are exponential.
Department of Management- Queuing Theory
Queue is formed because:-
The service facility is limited & the arrivals are infinite.
The mismatch between service facility & arrivals
TERMINOLOGY
QUEUEING SYSTEM
ARRIVAL PROCESS
CATEGORIES OF CUSTOMERS
SERVICE PROCESS
REPRESENTATION OF QUEUEING SYSTEM
NOTATION
Waiting Line Management Problem Solution, Writer Jacobs (1-15)Imran Hossain
This problem solution has been prepared by Abu Zafor, Abdus Salam and Imran Hossain of Islamic University, Kushtia of Management Department, Session: 2010-2011.
Department of Management- Queuing Theory
Queue is formed because:-
The service facility is limited & the arrivals are infinite.
The mismatch between service facility & arrivals
TERMINOLOGY
QUEUEING SYSTEM
ARRIVAL PROCESS
CATEGORIES OF CUSTOMERS
SERVICE PROCESS
REPRESENTATION OF QUEUEING SYSTEM
NOTATION
Waiting Line Management Problem Solution, Writer Jacobs (1-15)Imran Hossain
This problem solution has been prepared by Abu Zafor, Abdus Salam and Imran Hossain of Islamic University, Kushtia of Management Department, Session: 2010-2011.
MCM,MCA,MSc, MMM, MPhil, PhD (Computer Applications)
Working as Associate Professor at Zeal Education Society, Pune for MCA Progrmme.
Having 18 Years teaching experience
Talks about what is Queuing and its application, practical life usage, with a complex problem statement with its solution. Pre-emptive and non-preemptive queue models and its algorithm.
Queuing theory: What is a Queuing system???
Waiting for service is part of our daily life….
Example:
we wait to eat in restaurants….
We queue up in grocery stores…
Jobs wait to be processed on machine…
Vehicles queue up at traffic signal….
Planes circle in a stack before given permission to land at an airport….
Unfortunately, we can not eliminate waiting time without incurring expenses…
But, we can hope to reduce the queue time to a tolerable levels… so that we can avoid adverse impact….
Why study???? What analytics can be drawn??? Analytics means ---- measures of performance such as
1. Average queue length
2. Average waiting time in the queue
3. Average facility utilization….
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2. Introduction
Models to help managers understand and make decisions on the
operation of waiting lines.
Also known as a queue -- waiting line models are based on queueing
theory.
We are interested in the operating characteristics (a.k.a performance
characteristics) of waiting lines, which include the following:
1. The probability that no units are in the system.
2. The average number of units in the waiting line.
3. The average number of units in the system (number of units in
the waiting line + number being served)
4. The average time a unit spends in the waiting line.
5. The average time a unit spends in the system (waiting time +
service time)
6. The probability that an arriving unit has to wait for service.
3. General Waiting Line System Characteristics
Single Channel Waiting Line - Each customer entering an establishment passes through
one channel -- for example, one line and one order taking and filling station.
For most waiting line situations customer arrivals occur randomly and independently.
Quantitative analysts have found the Poisson distribution provides a good distribution
of the arrival pattern.
The probability function is as follows:
x = the number of arrivals in the time period
λ = the mean number of arrivals per time period (arrival rate)
e = 2.71828
While we can use this, in practice data should be recorded over a period of several days
or weeks and compared to the Poisson distribution.
4. General Waiting Line System Characteristics
Distribution of Service Times - the time a customer spends at a
service facility once a service has started.
Service time has been found to have an exponential probability
distribution.
µ = the mean number of units that can be served per time period (service rate)
e = 2.71828
Again, while we can use this, in practice data should be recorded over a period of
several days or weeks and compared to the Exponential distribution.
Additional Terms:
FCFS - First come first served -- this is the model we use in this section.
Transient Period - the beginning or start up period.
Steady-State Operation - normal state of operations.
5. Operating Characteristics - Single Channel Waiting Line Model with
Poisson Arrivals and Exponential Service Times
6. Operating Characteristics - Multiple Channel Waiting Line Model
with Poisson Arrivals and Exponential Service Times
These formulas are only applicable if:
1. The arrivals follow a Poisson
probability distribution
2. The service time for each channel
follows an exponential probability
distribution.
λ = the arrival rate
µ = service rate
k = number of channels