12. Consider a M/H2/1/FCFS/00/00 queue in steady state. Here H2 meansthat the service-time distribution is two-stage hyperexponential. Let A bethe arrival rate, and , the service rate of stage i (i = 1, 2). Suppose thatthe customer goes to stage 1 with probability of 0.5. Give an appropriatedefinition of the system state and draw the state transition diagram. Writedown the global balance equations for the general state and solve themusing z-transforms.%3D

In a M/H2/1 FCFS queue , where the service-time distribution is two-stage hyperexponential, and the…

Answered: 12. Consider a M/H₂/1/FCFS/00/0o queue…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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3. 3 jobs, with i.i.d. runtimes each U[0, 1], are to be run in parallel on 2 processors. By how much time does the expected flowtime decrease if the schedule is changed from a best fixed schedule to a best schedule with recourse?
1. i Now consider the M/M/1 queue with arrival rate λ and service rate µ and explain how it can be modelled as a birth death model. ii. For the M/M/1 queue derive the form of pn, the equilibrium distribution of the number of customers present, and give any conditions needed to ensure the existence of the equilibrium distribution. Derive the mean value of the equilibrium distribution
2. Two systems have a continuous load of 105 MW. Find the expected load loss (ELL) of each system if the generation is composed of : a. Six 20 MW hydro generating units each with an availability of 0.9. b. Five 25 MW thermal units each with an unavailability of 0.2.
9. Consider a bank office where customers arrive according to a Poisson process with an average arrival rate of customers per minute. The bank has only one teller servicing the arriving customers. The service time is exponentially distributed and the mean service rate is μ customers per minute. It turns out that the customers are impatient and are only willing to wait in line for an exponential distributed time with a mean of 1/μ minutes. Assume that there is no limitation on the number of customers that can be in the bank at the same time. a. Construct a rate diagram for the process and determine what type of queuing system this correspond to on the form A1/A2/A3. b. Determine the expected number of customers in the system when λ = 1 and μ = 2. c. Determine the average number of customers per time unit that leave the bank without being served by the teller when λ = 1 and µ = 2.
4. Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 1 using the Kaplan-Meir approach and interpret the results. Time in years Number at risk Nt Number of deaths, Dt Number of censored Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1 A) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85.B) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study.C) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment.D) The probability of surviving 1 year after being diagnosed with a slow-progressing form of…
a production line is producing light bulbs. 90% of the bulbs are good and .10% are defective. Suppose each bulbls condition is dependent of the other bulbs condition Select three buls at randon: 1. P(all 3 are good)=? 2. P( 2 of 3 are good)= 3. P(1 of 3 are good)=
6.
An organization for people with high IQ, and eligibility requires an IQ above 131.5. Suppose the IQ scores are normally distributed with a mean of 102.5 and standard deviation of 16.1. If someone wants to join the organization, what is the probability that he or she meets the organization’s requirement?
1. Suppose that for a stochastic variable X~B(n;p) with the parameters n =10 and p = 30% a) BY HAND (PICTURE MUST BE UPLOADED): Calculate the mean and the standard deviation b) Use IT to determine P(X = 4).

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