Find the minimum dynamic aggregate expected cost

Assignment Help Advanced Statistics
Reference no: EM13909509

Consider an integer-time queueing system with a finite buffer of size 2. At the beginning of the nth time interval, the queue contains at most two customers. There is a cost of one unit for each customer in queue (i.e., the cost of delaying that customer). If there is one customer in queue, that customer is served. If there are two customers, an extra server is hired at a cost of 3 units and both customers are served. Thus the total immediate cost for two customers in queue is 5, the cost for one customer is 1, and the cost for 0 customers is 0. At the end of the nth time interval, either 0, 1, or 2 new customers arrive (each with probability 1/3).

(a) Assume that the system starts with 0 ≤ ≤ 2 customers in queue at time -1 (i.e., in stage 1) and terminates at time 0 (stage 0) with a final cost of 5 units for each customer in queue (at the beginning of interval 0). Find the expected aggregate cost vi(1, u) for0 ≤ ≤ 2.

(b) Assume now that the system starts with customers in queue at time -2 with the same final cost at time 0. Find the expected aggregate cost vi(2, u) for 0 ≤ ≤ 2.

(c) For an arbitrary starting time -n, find the expected aggregate cost vi(nu) for 0 ≤ ≤ 2.

(d) Find the cost per stage and find the relative cost (gain) vector.

(e) Now assume that there is a decision maker who can choose whether or not to hire the extra server when there are two customers in queue. If the extra server is not hired, the three-unit fee is saved, but only one of the customers is served. If there are two arrivals in this case, assume that one is turned away at a cost of 5 units. Find the minimum dynamic aggregate expected cost v∗(1), 0 ≤ ≤ 2, for stage 1 with the same final cost as before.

(f) Find the minimum dynamic aggregate expected cost v∗(nu) for stage n,0 ≤ ≤ 2.

(g) Now assume a final cost of 1 unit per customer rather than 5, and find the new minimum dynamic aggregate expected cost v∗(nu), 0 ≤ ≤ 2.

Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.

Reference no: EM13909509

Questions Cloud

Bradford reagent and an equivalent volume : When preparing the protein standards, we used a tube (T) without protein, but including Bradford reagent and an equivalent volume of 0.15 M NaCl instead of protein. Can we just use plain water to prepare tube T instead?
Gorton argues that regulating capital ratios : 1. Gorton argues that regulating capital ratios cannot prevent a systemic run on banks.  true or false ? why ? 2. Over time banks have become more efficient at using bank capital and thus use less of it relative to the assets they fund. The capital r..
Direct labor and overhead are added evenly throughout : Belda Co. manufactures a single product in one department. Direct labor and overhead are added evenly throughout the process. Direct materials are added as needed.
Continental bank of illinois was bailed out before a banking : 1.Continental Bank of Illinois was bailed out before a banking crisis occurred. Regulators thought that Continental was too big to fail. true or false ? why ?2. Paul Volcker argued that the failure of Continental Illinois Bank would have caused other..
Find the minimum dynamic aggregate expected cost : Find the minimum dynamic aggregate expected cost v∗(n, u) for stage n,0 ≤ i ≤ 2. Find the cost per stage and find the relative cost (gain) vector.
Describe the legislative act : Describe the legislative act and analyze how it has influenced the U.S. health care system.
What are some of the mncs corporate characteristics : What are some of the MNCs corporate characteristics influencing its capital structure decisions?
Discussion on the value of the firm : Discussion on the Value of the Firm -   Subscribe Hide Description Please discuss the following: 1) Why the goal of Maximization of the Value of the Firm important for Corporations? 2) How would the firms go about achieving this goal?
Determine the firm''s cost of capital : Given the following information interest rate                        8% tax rate                              30%

Reviews

Write a Review

Advanced Statistics Questions & Answers

  Relationship between speed, flow and geometry

Write a project proposal on relationship between speed, flow and geometry on single carriageway roads.

  Logistic regression model

Compute the log-odds ratio for each group in Logistic regression model.

  Logistic regression

Foundations of Logistic Regression

  Probability and statistics

The tubes produced by a machine are defective. If six tubes are inspected at random , determine the probability that.

  Solve the linear model

o This is a linear model. If your model needs a different engine, then you need to rethink your approach to the model. Remember, there are no IF, Max, or MIN statements in linear models.

  Plan the analysis

Plan the analysis

  Quantitative analysis

State the hypotheses that you are going to test.

  Modelise as a markov chain

modelise as a markov chain

  Correlation and regression

What are the degrees of freedom for regression

  Construct a frequency distribution for payment method

Construct a frequency distribution for Payment method

  Perform simple linear regression

Perform simple linear regression

  Quality control analysis

Determining the root causes

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd