Operating characteristics ofqueuing system
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Queuing theory analyzes waiting lines and is essential for evaluating system performance across various fields such as operations research and manufacturing. It includes basic components like customer behavior, service processes, and system capacity, focusing on optimizing costs associated with waiting and idle times. Applications range from telecommunications to healthcare, impacting system efficiency and user experience.
![Total expected cost
Cost of providing
service
s
Increased service
Total expected cost = waiting time cost + cost of providing service
Let Cw = expected
waiting cost/unit time
Ls= expected no. of units
Cf = cost of servicing one unit
This will be minimum if d/dμ
(C)=0 Or if
-Cw.[λ/(μ-λ)²]+Cf=0 ,
Which gives ..
μ=λ±sqrt(Cw .λ/Cf)
Totalexpectedcostof
operatingfacility](https://image.slidesharecdn.com/operatingcharacteristicsofqueuingsystem-201116155635/85/Operating-characteristics-ofqueuing-system-15-320.jpg)
Operating characteristics ofqueuing system
- 1. operating characteristics of queuing system Aminul Islam Tanvin ID: 11509015 Department Of ICT
- 2. Queuing Theory • Queuing theory is the mathematics of waiting lines. • It is extremely useful in predicting and evaluating system performance. • Queuing theory has been used for operations research, manufacturing and systems analysis. Traditional queuing theory problems refer to customers visiting a store, analogous to requests arriving at a device.
- 3. Queuing problems arises because either There is too less demand (Much idle facility time or too Many facilities The problem is to either schedule arrivals or provide extra facilities or both so as to obtain an optimum balance between costs associated with waiting time and idle time . There is too much demand on the facilities
- 4. Basic elements of Queuing System •Entries or customers •Queue (waiting lines) •Service channels or service facility
- 6. Service process Arrival process Customer’s Behavior Queue Discipline Number of servers System capacity characteristics of queuing system Operating Characteristics Of Queue
- 7. Arrival pattern •Customers arrive in scheduled or random fashion. •The time duration between each customers’ arrival is known as inter arrival time. We assume it to follow Poisson Distribution Poisson Distribution probability Arrival per unit time(λ)
- 8. Exponential Distribution Service Pattern •Number of servers and speed of service to be considered. •The time taken by a server to service a customer is known as Service Time. It is represented by Exponential Distribution probability Customer served per unit time (μ) Assumption: λ<μ
- 9. Service Channels Single channel queuing system Multi channel queuing system Single channel multi phase system Multi channel multi phase system
- 10. Service Discipline • FCFS (First-Come-First-Served) • LCFS (Last-Come-First-Served) • Service in random order • Priority service
- 11. System Capacity • Maximum number of customers that can be accommodated in the queue. • Assumed to be of infinite capacity.
- 12. Customer’s Behavior • Balking- When a customer leaves the queue because it is too long, has no time to wait, no space to stand etc. • Reneging- When a customer leaves the queue because of his impatience. • Jockeying- When a customer shifts from one queue to another.
- 13. Service Facility Behavior •Failure: A server may fail while serving a customer, thereby interrupting service untill a repair can be made. •Changing service rate: A server may speed up or slow down, depending on the number of customers in the queue. •Batch processing: A server may service several customers simultaneously.
- 14. Waiting and Idle time costs Cost of waiting customers Cost of idle service facility • Indirect cost of business loss • Direct cost of idle equipment or person. • Payment to be made to the servers(engaged at the facilities),for the period for which they remain idle. The optimum balance of costs can be made by scheduling the flow of units or providing proper number of service facilities .
- 15. Total expected cost Cost of providing service s Increased service Total expected cost = waiting time cost + cost of providing service Let Cw = expected waiting cost/unit time Ls= expected no. of units Cf = cost of servicing one unit This will be minimum if d/dμ (C)=0 Or if -Cw.[λ/(μ-λ)²]+Cf=0 , Which gives .. μ=λ±sqrt(Cw .λ/Cf) Totalexpectedcostof operatingfacility
- 16. Transient & Steady State of the system • When the operating characteristics are dependent on time, it is said to be a transient state. • When the operating characteristics are independent of time, it is said to be a steady state.
- 17. Traffic intensity The ratio λ/μ is called the traffic intensity or the utilization factor and it determines the degree to which the capacity of service station is utilized.
- 18. Applications of Queuing Model • Telecommunications • Traffic control • Determining the sequence of computer operations. • Predicting computer performance • Health services (e.g.. control of hospital bed assignments) • Airport traffic, airline ticket sales • Layoutof manufacturing systems.