1. Advantages of simulation 1. New policies, operating procedures, information flows and son on can be explored without disrupting ongoing operation of the real system. 2. New hardware designs, physical layouts, transportation systems and … can be tested without committing resources for their acquisition. 3. Time can be compressed or expanded to allow for a speed-up or slow-down of the phenomenon( clock is self-control). 4. Insight can be obtained about interaction of variables and important variables to the performance. 5. Bottleneck analysis can be performed to discover where work in process, the system is delayed. 6. A simulation study can help in understanding how the system operates. 7. “What if” questions can be answered.

2. Disadvantages of simulation 1. Model building requires special training. 2. Simulation results can be difficult to interpret. 3. Simulation modeling and analysis can be time consuming and expensive. 4. Many simulation software have output- analysis.

3. Discrete and Continues Systems  A discrete system is one in which the state variables change only at a discrete set of points in time : Bank example

4. Discrete and Continues Systems (cont.)  A continues system is one in which the state variables change continuously over time: Head of water behind the dam

5. Queuing Theory

6. Definitions 1. System : is a collection of entities which are logically related and which are of interest to a particular application. 2. Entit y An object of interest in the system : Machines in factory 3. Attribut e The property of an entity : speed, capacity 4. Activity A time period of specified length :welding, stamping 5. State A collection of variables that describe the system in any time : status of machine (busy, idle, down,…) 6. Event A instantaneous occurrence that might change the state of the system

7. INTRODUCTION  A queuing system consists of one or more servers that provide service of some sort to arriving customers.  Customers who arrive to find all servers busy generally join one or more queues (lines) in front of the servers, hence the name queuing systems.  There are several everyday examples that can be described as queuing systems, such as bank-teller service, computer systems, manufacturing systems, maintenance systems, communications systems and so on.

8. Components of a Queuing System:

9.  1- Population of Customers can be considered either limited (closed systems) or unlimited (open systems).  Unlimited population represents a theoretical model of systems with a large number of possible customers (a bank on a busy street, a motorway petrol station).  Example of a limited population may be a number of processes to be run (served) by a computer or a certain number of machines to be repaired by a service man  Customers may be people, machines of various nature, computer processes, telephone calls,

10. Components of a Queuing System:  2- Arrival defines the way customers enter the system. Mostly the arrivals are random with random intervals between two adjacent arrivals. Typically the arrival is described by a random distribution of intervals also called Arrival Pattern.

11. Components of a Queuing System:  3- Queue represents a certain number of customers waiting for service (of course the queue may be empty).  The customer being served is considered not to be in the queue.  There are two important properties of a queue: Maximum Size and Queuing Discipline

12. Components of a Queuing System:  Maximum Queue Size (also called System capacity) is the maximum number of customers that may wait in the queue (plus the one(s) being served).  Queue is always limited, but some theoretical models assume an unlimited queue length. If the queue length is limited, some customers are forced to renounce without being served

13. Components of a Queuing System:  Service represents some activity that takes time and that the customers are waiting for.  Output represents the way customers leave the system. Output is mostly ignored by theoretical models, but sometimes the customers leaving the server enter the queue again

14. Components of a Queuing System:  Queuing Discipline represents the way the queue is organized (rules of inserting and removing customers to/from the queue).  The ways are these ways: 1) FIFO (First In First Out) also called FCFS (First Come First Serve) - orderly queue. 2) LIFO (Last In First Out) also called LCFS (Last Come First Serve) - stack. 3) SIRO (Serve In Random Order). 4) Priority Queue, that may be viewed as a number of queues for various priorities.