Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2013
1.
States: (0) and (n,a), (n,b) for n=1,2,3 where n is the number of items in the system (in queue
and in service), and a indicates the machine is in operation, b the machine is interrupted.
Transitio
Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2013
ISE 230, Solution of Homework 3
Question 1.
a)
The rate diagram is:
b)
In order to obtain the steady state probabilities, consider the balance equations:
For node 0:
4
40 = 51 1 = 0
5
For node 1:
12
3
Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2013
NAME:
ISE230 Introduction to Stochastic Models in Operations Research
Prof. B. Defourny Lehigh University
_
Final Wednesday December 17, 2014, 12:00pm 1:30pm
Question 1/3
Compare the two following M/
Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2013
ISE 230: Solution HW 2
1)
checkout stand
fire station
toll booth
Bike repair shop
shipping dock
machines for one operator
materials handling
equipment
Plumbing shop
custom order job shop
secretarial t
Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2013
FIRST NAME:
1
LAST NAME:
ISE230 Introduction to Stochastic Models in Operations Research
Prof. B. Defourny Lehigh University
Final Exam
Wednesday Dec. 11, 2013, 7:10pm10:00pm.
Question 1: Decision a
Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2013
ISE230 IMMuLOII to Stochastic Models in Operations Research
Prof. B. Defourny Lehigh University
Midterm I Thursday Oct. 3, 2013, 7:55am9:05am.
Question 1/4
Consider the birthand ~; 1 process with
Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2013
Solutions Final 2015
Q1
1) 3 classes: (0,1), (2), (3,4,5,6)
2) 0,1 are transient and aperiodic, 2 to 6 are recurrent, 3 to 6 are periodic
(period 2), 2 is absorbing.
3) the Markov chain is reducible a
Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2014
Erin Ricker
8/28/14
ISE 230 HW 1
1. Valley Farm Market has a parking lot with 3 parking spots reserved for its
customers. During the opening hours of this grocery store, cars enter the lot
and use one
Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2013
ISE230 Fall 2016  Prof. B. Defourny  Homework 11
Question 1
Consider the discretetime, finite Markov Chain described as (0 , ) where 0 is the row
vector of initial state probabilities with element
Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2013
ISE230 Fall 2016  Prof. B. Defourny  Homework 9
Question 1
Compute the reliability R(t) of the component with failure rate h(t) = 3 .
We have 0 () = 0 3 = [ 3 3]0 = ( 3 1)3 thus () = (
3 1)3
Questi
Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2013
ISE230 Fall 2016  Prof. B. Defourny  9/19 Quiz
Consider an M/M/1 queue where the probability of having 4 customers waiting in queue is 0.3, and the
probability of having 2 customers waiting in queu
Introduction to Stochastic Models in Operations Researc
ISE 230

Fall 2013
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