Question

Jobs Needing Repair A system consists of a service facility and a repair facility. The service time at both facilities is Exp($\frac{1}{10}$). Jobs arrive at the service facility according to a Poisson process with rate λ. After each visit to the service facility, the job either: • leaves the system (probability 0.1) • requires repair (probability 0.01) • revisits the service facility (probability 0.89). After completing repair, a job returns to the service facility, except that now, after each visit to the service facility, the job either: • leaves the system (probability 0.1) • requires repair (probability 0.5) • revisits the service facility (probability 0.4). Please answer the following questions about the system: (a) What is the expected number of times that a job visits the service facility? (b) What is the highest possible throughput, λ? (c) Set λ = $\frac{1}{200}$. What is the expected time in system, E[T]?

Name: jobs needing repair a system consists of a service facility and a repair facility the service time at both facilities is expfrac110 jobs arrive at the service facility according to a poisson 23657
Uploaded: 2024-02-01T02:56:58-08:00
Duration: 1 min 29 s
Channel: Lien Le
Description: jobs needing repair a system consists of a service facility and a repair facility the service time at both facilities is expfrac110 jobs arrive at the service facility according to a poisson 23657

          Jobs Needing Repair
A system consists of a service facility and a repair facility. The service time at both facilities is Exp($\frac{1}{10}$). Jobs arrive at the service facility according to a Poisson process with rate λ. After each visit to the service facility, the job either:
• leaves the system (probability 0.1)
• requires repair (probability 0.01)
• revisits the service facility (probability 0.89).
After completing repair, a job returns to the service facility, except that now, after each visit to the service facility, the job either:
• leaves the system (probability 0.1)
• requires repair (probability 0.5)
• revisits the service facility (probability 0.4).
Please answer the following questions about the system:
(a) What is the expected number of times that a job visits the service facility?
(b) What is the highest possible throughput, λ?
(c) Set λ = $\frac{1}{200}$. What is the expected time in system, E[T]?

$jobs needing repair a system consists of a service facility and a repair facility the service time at both facilities is expfrac110 jobs arrive at the service facility according to a poisson 23657$

Added by Amber L.

Question

Please give Ace some feedback