Queuing theory - Priority queuing models

6 important questions on Queuing theory - Priority queuing models

What is meant with priority queuing models?

Models in which the customers type determines the order in which  customers undergo service.

In priority queuing models say something about:
  • Interarrival times;
  • Interarrival times different customers;
  • Description service time;
  • the ranking of i;

  • Interarrival times of type i customers are exponential;
  • Interarrival times of different customers are independent;
  • Service time is described by random variable Si;
  • Lower numbered i has priority over higher numbered;

What is a nonpreemptive priority model?

A customer service cannot be interrupted. After each service completion the next customer to enter service is chosen by giving priority to lower-numbered customer types.

In the kendall lee notation, this is labelled by the 4th characteristic being NPRP.   By indicating multiple customers the first two characteristics are indicated with i's Mi/Gi etc.
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Considering nonpreemptive priority queuinig models, what does the following mean?
  • Wqk
  • Wk
  • Lqk
  • Lk  

Wqk = waiting time in line spent by a type k customer;

wk = state time in the system spent by a type k customer;

Lqk = state numberof type customers waiting in line;

Lk = state number of type k customers in the system;

Considering a nonpreemptive queuing model, how do you calculate Wqk, Lqk, Wk and Lk?

See image.

What is the definition of a preemptive priority?

In a preemptive priority queuing system a lower priority customer can be bumped from service whenever a higher-priority customer arrives.

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