# Question: Consider the single server variation of the nonpreemptive priorities model presented

Consider the single-server variation of the nonpreemptive priorities model presented in Sec. 17.8. Suppose there are three priority classes, with λ1 = 1, λ2 = 1, and λ3 = 1. The expected service times for priority classes 1, 2, and 3 are 0.4, 0.3, and 0.2, respectively, so μ1 = 2.5, μ2 = 3 1/3, and μ3 =] 5.

(a) Calculate W1, W2, and W3.

(b) Repeat part (a) when using the approximation of applying the general model for nonpreemptive priorities presented in Sec. 17.8 instead. Since this general model assumes that the expected service time is the same for all priority classes, use an expected service time of 0.3 so μ = 3 1/3. Compare the results with those obtained in part (a) and evaluate how good an approximation is provided by making this assumption.

(a) Calculate W1, W2, and W3.

(b) Repeat part (a) when using the approximation of applying the general model for nonpreemptive priorities presented in Sec. 17.8 instead. Since this general model assumes that the expected service time is the same for all priority classes, use an expected service time of 0.3 so μ = 3 1/3. Compare the results with those obtained in part (a) and evaluate how good an approximation is provided by making this assumption.

**View Solution:**## Answer to relevant Questions

Consider a single-server queueing system with any servicetime distribution and any distribution of interarrival times (the GI/G/1 model). Use only basic definitions and the relationships given in Sec. 17.2 to verify the ...Read the referenced article that fully describes the OR study summarized in the application vignette presented in Sec. 17.9. Briefly describe how queueing theory was applied in this study. Then list the various financial and ...Jim McDonald, manager of the fast-food hamburger restaurant McBurger, realizes that providing fast service is a key to the success of the restaurant. Customers who have to wait very long are likely to go to one of the other ...A three-server queueing system has a controlled arrival process that provides customers in time to keep the servers continuously busy. Service times have an exponential distribution with mean 0.5. You observe the queueing ...Consider the birth-and-death process with the following mean rates. The birth rates are λ0 = 2, λ1 = 3, λ2 = 2, λ3 = 1, and λn = 0 for n > 3. The death rates are μ1 = 3, μ2 = 4, μ3 = 1, and μn = 2 for n > 4. (a) ...Post your question