Compute the expected queueing time in a G/M/1 queue with a service rate of 10 per hour and the following inter-arrival time distributions, all with mean 8 minutes: (1) exponential; (2) deterministic. Which distribution produces the smallest Wq and which the largest?
Added by Aitor S.
Close
Step 1
The expected queueing time in a G/M/1 queue with a service rate of 10 per hour and Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 93 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Suppose that a queue has $n$ servers and that the length of time to complete a job is an exponential random variable. If a job is at the top of the queue and will be handled by the next available server, what is the distribution of the waiting time until service? What is the distribution of the waiting time until service of the next job in the queue?
a-) You are given an M/M/1 queuing system with mean arrival rate λ and mean service rate μ. An arriving customer receives n dollars if n customers are already in the system. Determine the expected cost in dollars per customer. b-) You are given an M/M/1 queuing system in which the expected waiting time and expected number in the system are 120 minutes and 8 customers, respectively. Determine the probability that a customer's service time exceeds 20 minutes.
Rashmi S.
Consider a two-server queuing system where all service times are independent and identically distributed according to an exponential distribution with a mean of 10 minutes. Service is provided on a first-come-first-served basis. When a particular customer arrives, he finds that both servers are busy and no one is waiting in the queue. (a) (10 points) What is the probability distribution of this customer's waiting time in the queue? (b) (5 points) Determine the expected value of this customer's system time. (c) (10 points) Suppose that this customer is still waiting in the queue 5 minutes after his arrival. Given this information, determine the expected value of this customer's system time.
Shaiju T.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD