Question: For the queueing system of Section 3.61 define V(t), the work in the system at time, as the sum of the remaining service times of

For the queueing system of Section 3.61 define V(t), the work in the system at time, as the sum of the remaining service times of all customers in the system at Let V = lim V(s) ds/t. 00+ Also, let D, denote the amount of time the ith customer spends waiting in queue and define W = lim (D, + + Dn)/n 11-%

(a) Argue that V and Wo exist and are constant with probability 1.

(b) Prove the identity V=E[Y]WQ+E[Y]/2,

where 1/A is the mean interarrival time and Y has the distribution of a service time.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Probability And Stochastic Modeling Questions!

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Please find attached the case study 2: A troubled Project at Modern Materials Inc. Page 498-505 for this assignment. You will critically analyze the attached case study: A troubled Project at Modern...

Please Anwser following QUESTIONS. 1.Identify the Challenges - Provide for a brief description of the challenges that the organization is facing and how they are planning to address them. This...

1) What are Netflix's resources, capabilities, and core competencies in this case based on the VRIO framework? 2) Conduct a SWOT analysis based on the case. It's not Netflix that's making the...

2. For a single-server queueing system (e.g. one-operator barbershop), define L(t) to be the total number of customers in the system at time t (including the queue and the customer in service at time...

corporate culture and strategy 1 how do interpret the phrase "Culture eats strategy for lunch"? 2. With respect to the BP case, Identity 3 failures of leadership andar corporate culture that...

\fCHAPTER 14 Server Farms: M/M/k and M/M/k/k In today's high-volume world, almost no websites, compute centers, or call centers consist of just a single server. Instead a \"server farm\" is used. The...

Introduction and learning objectives When you were learning about operational analysis earlier in the term, we talked about jobs that require multiple visits to the CPU (or servers) to receive their...

The function h is defined below. h(x)= x+2x-8 x+2x-63 X = E Find all values of X that are NOT in the domain of If there is more than one value, separate them with

Let A, B, and C denote the three vertices of a triangle. If F is the midpoint of side AC, show that FE = +AB.

EC 1 . In a prison, there is a door b / w any pair of adjacent cells and one exit guarded by a guard G . One prisoner is a maniac M which kills anybody he can see when he enters a cell. If M returns...

The lack of innovation and entrepreneurial focus at American Express (AmEx) may be because of hubris, inertia, and a lack of capability. The firms performance in 2014 was not, by any means, what...

Suppose that coin 1 has probability 0.7 of coming up heads, and coin 2 has probability 0.6 of coming up heads. If the coin flipped today comes up heads, then we select coin 1 to flip tomorrow, and if...

In Example 4.4 suppose that it has rained neither yesterday nor the day before yesterday. What is the probability that it will rain tomorrow?

Let the transition probability matrix of a two-state Markov chain be given, as in Example 4.2, by P 1- P = 1-p P Show by mathematical induction that p(x) +(2p 1)-(2p - 1)" -

Using a global strategy, GreenSmile Inc. offers standardized products across country markets, with the competitive strategy being dictated by offices within the host markets served. True False

Perry started Perry's Carpentry Company in 2020 with the financial year ended on December 31. The financial statements of Perry's Carpentry are as follows: Perry's Carpentry Income Statement For the...

Various equipment was purchased and placed in service this year in the amount of $3,000,000. Taxable income before the 179 deduction was $800,000. Indicate the amount of deduction under the Section...