Queuing Theory

In: Business and Management

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Queuing Theory

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. Traditional queuing theory problems refer to customers visiting a store, analogous to requests arriving at a device.

Long Term Averages
• Queuing theory provides long term average values. • It does not predict when the next event will occur. • Input data should be measured over an extended period of time. • We assume arrival times and service times are random. • • • •

Independent arrivals Exponential distributions Customers do not leave or change queues. Large queues do not discourage customers. Many assumptions are not always true, but queuing theory gives good results anyway

Queuing Model
Q W λ Tw

Interesting Values
• Arrival rate (λ) — the average rate at which customers arrive. • Service time (s) — the average time required to service one customer. • Number waiting (W) — the average number of customers waiting. • Number in the system (Q) — the average total number of customers in the system.

More Interesting Values
• Time in the system (Tq) the average time each customer is in the system, both waiting and being serviced. Time waiting (Tw) the average time each customer waits in the queue. Tq = Tw + s

Arrival Rate
• The arrival rate, λ, is the average rate new customers arrive measured in arrivals per time period. Common units are access/second • The inter-arrival time, a, is the average time between customer arrivals. It is measured in time per customer. A common unit would be seconds/access.


Random Values
• We assume that most of the events we are interested in occur randomly.
– Time of a request to a device – Time to service a request – Time user makes a request


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