ZeePedia

Queuing Theory:DEFINITION OF TERMS IN QUEUEING MODEL

<< Assignment Problems:SOLUTION OF AN ASSIGNMENT PROBLEM
Queuing Theory:SINGLE-CHANNEL INFINITE-POPULATION MODEL >>
img
Operations Research (MTH601)
226
INTRODUCTION
It is a common phenomenon in everyday life to see a large number of persons waiting in front of a
booking counter in a railway station or in a theatre or in a ration shop to have some service carried out. This
formation of queue occurs whenever the present demand for a service exceeds the present capacity to provide
the necessary government, industry, schools, hospitals, etc.
A decision regarding the amount of capacity to provide must be made frequently in industry and other
places. It is difficult to predict about an arrival and the type of service required. If we provide too much service,
it would involve unnecessary excessive costs. On the otherhand, if we do not provide enough service capacity,
this will result in a long waiting line, which proves costly. So we are interested in reaching an economic balance
between the cost of service and the cost associated with waiting for the service. Queuing theory or waiting line
theory provides vital information required for such a decision. For describing a waiting line situation queuing
theory provides a number of alternative mathematical models.
The basic queuing system consists of two major components as shown in figure 1. Customers arriving
at a queuing system wait in queue to get some service, or if the system is idle or empty, the arriving customer
may be serviced immediately. Once the service is over the customer leaves the system.
Served Units
Service
Queue
Input
Source
Served Units
The Basic Queuing System
DEFINITION OF TERMS IN QUEUEING MODEL
Customer:  The arriving unit that requires some service to be provided is called the customer. The
customer may represent people, machines, etc.
Server: A server is one who provides the arriving customer the necessary service. It may be persons
in the counter or machines, etc.
Waiting Line or Queue: The queue represents the number of customers waiting to be served.
Normally the queue does not include the customer being served.
Service Channel: This refers to the type of service provided. If we have one serving unit only, we
have a single channel model or single server model. If service involves more than one server, we have a multi-
channel server model. We use the symbol k to denote the number of service channels.
226
Table of Contents:
  1. Introduction:OR APPROACH TO PROBLEM SOLVING, Observation
  2. Introduction:Model Solution, Implementation of Results
  3. Introduction:USES OF OPERATIONS RESEARCH, Marketing, Personnel
  4. PERT / CPM:CONCEPT OF NETWORK, RULES FOR CONSTRUCTION OF NETWORK
  5. PERT / CPM:DUMMY ACTIVITIES, TO FIND THE CRITICAL PATH
  6. PERT / CPM:ALGORITHM FOR CRITICAL PATH, Free Slack
  7. PERT / CPM:Expected length of a critical path, Expected time and Critical path
  8. PERT / CPM:Expected time and Critical path
  9. PERT / CPM:RESOURCE SCHEDULING IN NETWORK
  10. PERT / CPM:Exercises
  11. Inventory Control:INVENTORY COSTS, INVENTORY MODELS (E.O.Q. MODELS)
  12. Inventory Control:Purchasing model with shortages
  13. Inventory Control:Manufacturing model with no shortages
  14. Inventory Control:Manufacturing model with shortages
  15. Inventory Control:ORDER QUANTITY WITH PRICE-BREAK
  16. Inventory Control:SOME DEFINITIONS, Computation of Safety Stock
  17. Linear Programming:Formulation of the Linear Programming Problem
  18. Linear Programming:Formulation of the Linear Programming Problem, Decision Variables
  19. Linear Programming:Model Constraints, Ingredients Mixing
  20. Linear Programming:VITAMIN CONTRIBUTION, Decision Variables
  21. Linear Programming:LINEAR PROGRAMMING PROBLEM
  22. Linear Programming:LIMITATIONS OF LINEAR PROGRAMMING
  23. Linear Programming:SOLUTION TO LINEAR PROGRAMMING PROBLEMS
  24. Linear Programming:SIMPLEX METHOD, Simplex Procedure
  25. Linear Programming:PRESENTATION IN TABULAR FORM - (SIMPLEX TABLE)
  26. Linear Programming:ARTIFICIAL VARIABLE TECHNIQUE
  27. Linear Programming:The Two Phase Method, First Iteration
  28. Linear Programming:VARIANTS OF THE SIMPLEX METHOD
  29. Linear Programming:Tie for the Leaving Basic Variable (Degeneracy)
  30. Linear Programming:Multiple or Alternative optimal Solutions
  31. Transportation Problems:TRANSPORTATION MODEL, Distribution centers
  32. Transportation Problems:FINDING AN INITIAL BASIC FEASIBLE SOLUTION
  33. Transportation Problems:MOVING TOWARDS OPTIMALITY
  34. Transportation Problems:DEGENERACY, Destination
  35. Transportation Problems:REVIEW QUESTIONS
  36. Assignment Problems:MATHEMATICAL FORMULATION OF THE PROBLEM
  37. Assignment Problems:SOLUTION OF AN ASSIGNMENT PROBLEM
  38. Queuing Theory:DEFINITION OF TERMS IN QUEUEING MODEL
  39. Queuing Theory:SINGLE-CHANNEL INFINITE-POPULATION MODEL
  40. Replacement Models:REPLACEMENT OF ITEMS WITH GRADUAL DETERIORATION
  41. Replacement Models:ITEMS DETERIORATING WITH TIME VALUE OF MONEY
  42. Dynamic Programming:FEATURES CHARECTERIZING DYNAMIC PROGRAMMING PROBLEMS
  43. Dynamic Programming:Analysis of the Result, One Stage Problem
  44. Miscellaneous:SEQUENCING, PROCESSING n JOBS THROUGH TWO MACHINES
  45. Miscellaneous:METHODS OF INTEGER PROGRAMMING SOLUTION