X120635
Stochastic Models in Operations Research
Jun LUO
Assigned May. 14, 2016
Due May. 27, 2016
Homework Seven
1. Assume cfw_B(t), t 0 is a standard Brownian motion process. Compute E[B(t1 )B(t2 )B(
CPU
(scheduler)
(scheduling algorithm)
A new process starts
The running process exits
The running process is blocked
I/O interrupt (some processes will be ready)
Clock interrupt (every 10 mill
Demand Paging:
Bring a page into memory only when it is needed (on demand)
Page is needed <=> bring to memory

+> Page Fault
Lazy swapper never swaps a page into memory
unless page will be needed
W
Case Study: UNIX
UNIX
=
Linux
.

Computer Systems  A Programmers Perspective
<>
Professional Assembly Language
Richard Blum
UNIX
UNIX
=
=> AT&T
1. UNIX
=>
Unix grew out of Multics
Commercial U
7.
IPC
UNIX System V
(XSI)
=> MINIX
shmget( );
shmctl( );
=> int shmget(key_t key, size_t size, int flag);
shmat( );
Returns: shared memory ID if OK, 1 on error
shmdt( );
void *shmat(int shmid, con
X120635
Stochastic Models in Operations Research
Assigned Apr. 9, 2016
Jun LUO
Due Apr. 22, 2016
Homework Four
1. Consider a general birth and death process with birth rates n and death rates n , wher
X120635
Stochastic Models in Operations Research
Assigned Apr. 23, 2016
Jun LUO
Due May. 6, 2016
Homework Five
1. Suppose that customers arrive at a specified store in accordance with a renewal proces
X120635
Stochastic Models in Operations Research
Assigned Mar. 12, 2016
Jun LUO
Due Mar. 25, 2016
Homework Two
1. Independent trials, each of which is a success with probability p, are performed until
X120635
Stochastic Models in Operations Research
Assigned Mar. 26, 2016
Jun LUO
Due Apr. 8, 2016
Homework Three
1. Suppose the numbers of families that check into a hotel on successive days are indepe
X120635
Stochastic models in Operations Research
Assigned Feb. 29, 2016
Jun LUO
Due Mar. 11, 2016
Homework One
1. The probability of winning on a single toss of the dice is p. A starts, and if he
fail
Solutions to Homework Six
1. For an M/M/1 queue in steady state, let Na be the number of customers the next arrival
will find in the system. What is the probability P cfw_Na = n and E[Na ] ?
Solution:
Solutions to Homework Three
1. Suppose the numbers of families that check into a hotel on successive days are independent Poisson random variables with mean . Also suppose that the number
of days that
Solutions to Homework Two
1. Independent trials, each of which is a success with probability p, are performed until there
are k consecutive successes. What is the mean number of necessary trials ?
Sol
Solutions to Homework Four
1. Consider a general birth and death process with birth rates n and death rates n , where
0 = 0, and let Ti denote the time, starting from state i, it takes for the process
X120635
Stochastic Models in Operations Research
Assigned May. 2, 2016
Jun LUO
Due May. 13, 2016
Homework Six
1. For an M/M/1 queue in steady state, let Na be the number of customers the next arrival
Solutions to Homework Five
1. Suppose that customers arrive at a specified store in accordance with a renewal process
having interarrival distribution F . Suppose that the store stocks a single type o