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# Queuing Theory

queuing theory mathematical modelling algorithm applications

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### Queuing Theory

1. 1. IT-319 SEMINAR PRESENTATION By: Rishita Jaggi 1140213 IT-3
2. 2. What is QUEUE?  Any system where jobs arrive looking for service and depart once service is provided is described as a queue.  The Queuing theory provides predictions about waiting times, the average number of waiting customers, the length of a busy period and so forth.
3. 3. Queue Representation
4. 4. System Customers Server Reception desk People Receptionist Hospital Patients Nurses Airport Airplanes Runway Road network Cars Traffic light Grocery Shoppers Checkout station Computer Jobs CPU, disk, CD Queuing examples
5. 5. CHARACTERISTICS Arrival Pattern Service Pattern Queue Discipline System Capacity Service Channels
6. 6. SIMULATION OF QUEUE
7. 7. EXAMPLE: AT=[0,10,15,35,30,10,5,5] ST=[20,15,10,5,15,15,10,10]
8. 8. M/M/1 QUEUING SYSTEM
9. 9. Assumptions of M/M/1 Queuing System  The number of customers in the system is very large.  Impact of a single customer on the performance of the system is very small.  All customers are independent.  A single server for the queue.  The queue discipline for this system is FIFO.
10. 10. Mathematical Modeling Putting n=0 •t is used to define the interval 0 to t •n is the total number of arrivals in the interval 0 to t. •lambda is the total average arrival rate in arrivals/sec.
11. 11. Cars On a Highway Consider a highway with an average of 1 car arriving every 10 seconds (0.1 cars/second arrival rate). The probability distribution with t is given.
12. 12. M/M/1 Results ρ = λ / µ •rho is occupancy (traffic intensity) •mu is average service rate. •N is mean number of customers. •T is total waiting time.
13. 13. APPLICATIONS Banking Sector Telephone System Computer Networks Computer Systems Toll Booths etc.