he arrival rate of patients at a hospital counter follows Poisson distribution with a mean of 25 per hour. The service rate of the treatment to patients also follows Poisson distribution with a mean of 45 per hour. What is the probability of having 0 patients in the system (P 0 )? What is the probability of having 10 patients in the system (P 10 )? What is the probability of having 15 patients in the system (P 15 )? Find Ls, Lq, Ws and Wq

he arrival rate of patients at a hospital counter follows Poisson distribution with a mean of 25 per hour. The service rate of the treatment to patients also follows Poisson distribution with a mean of 45 per hour. What is the probability of having 0 patients in the system (P 0 )? What is the probability of having 10 patients in the system (P 10 )? What is the probability of having 15 patients in the system (P 15 )? Find Ls, Lq, Ws and Wq

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 35P

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The arrival rate of patients at a hospital counter follows Poisson distribution with a mean of 25 per hour. The service rate of the treatment to patients also follows Poisson distribution with a mean of 45 per hour. What is the probability of having 15 patients in the system (P 15 )?
The arrival rate of patients at a hospital counter follows Poisson distribution with a mean of 25 per hour. The service rate of the treatment to patients also follows Poisson distribution with a mean of 45 per hour.a) What is the probability of having 0 patients in the system (P 0 )?
In an M/M/1 queueing system, the arrival rate is 5 customers per hour and the service rate is 7 customers per hour. What is the expected number of customers in the system (L)? (Round your answer to 3 decimal places.) What is the expected waiting time in the system (W)? (Express the waiting time in hours, round your answer to 3 decimal places.) What is the expected number of customers in the queue(Lq)? (Round your answer to 3 decimal places.) What is the expected waiting time in the queue(Wq)? (Express the waiting time in hours, round your answer to 3 decimal places.)
The common measures of a queuing system's performance include: O probability that the service facility will be idle, average queue length, and probability that the waiting time will exceed a specified duration. average time each customer spends in the system, probability that the service system will be idle, and average time each customer spends in the queue. average queue length, maximum time a customer may spend in the queue, and the utilization factor for the system. average time each customer spends in the system, maximum queue length, and probability of a specific number of customers in the system. maximum queue length, maximum time a customer may spend in the queue, and average queue length.