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Questions of simulation 1) Components of a system Name several entities, attributes, activities, events, and state variables for the following systems: 2

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Questions of simulation
1) Components of a system Name several entities, attributes, activities, events, and
state variables for the following systems:
2. Manual Simulation
A taxi company operates one vehicle during 01:00 to 12:00 o’clock. Currently, consideration is being given to the addition of a second vehicle to the fleet. The demand for
taxis and time to complete a service follow the distribution shown in the table below.

Time between calls [Minute]	15	20	25	30	35
Probability between calls	0.15	0.20	0.45	0.15	0.05
Service time [Minute]	5	15	25	35	45
Probability of service time	0.15	0.35	0.40	0.06	0.04

(a) Simulate ten (10) individual days of operation of the current system and of the
system with an additional taxicab.
(b) Compare the two systems with respect to the waiting times of the customer and
any other measures that might shed light on the situation.
3. Statistical Models in Simulation
(a) Customers at a restaurant arrive in groups (one to eight persons). The number of
persons(per group) for 300 customers and the relative frequencies are given below.
Draw the empirical cumulative distribution function (cdf).
Jimma University, Jimma Institute of Technology
Faulty of Electrical and Computer Engineering
(a) A cafeteria
(b) A grocery store
(c) A fast-food restaurant
(d) A hospital emergency room
(e) A taxicab company with 10 taxis
(f) A local area network (LAN)
(g) A wireless local area network (WLAN) installation with 3 Access Points (AP).
(h) A desktop computer
Computer System Modeling and Simulation
Programme: M.Sc in Computer Engineering Year: I, Sem.: I, 2021
Assignment Mark: 50

Arrival per party	1	2	3	4	5	6	7	8
Frequency	30	110	45	71	12	13	7	12

(b) A hurricane is to hit in country, and expected to follow Poisson distribution with a
mean of 08 per year.
i. computer the probability of exactly one hurricane in a year will be.
ii. Compute the probability of more than two hurricane in one year will be.
(c) The lifetime, in years, of a satellite place in orbit is given be exponential distribution
with λ = 0:4.
i. what is the probability of the satellite lasting atleast five years?
ii. what is the probability that the satellite dies between three and six years?
(d) The time to failure of a battery is Weibull distributed with parameters (β = 1=4; α =
1=2 years; ν = 0)
i. Find the probability that the battery will fail within 1.5 years.
ii. Find the probability that battery will last for longer than its mean life.
iii. Find the probability that battery will last between 1.5 and 2.5 years.
4. Linear Congruential Generator
For 16-bit computers it was recommended to combine three multiplicative generators
with m1 = 32363, α1 = 157, m2 = 31727,α2 = 146, m3 = 31657, and α3 = 142. The
period of this generator is approximately 8 × 1012.
(a) Generate 10 random numbers with the combined generator, using the initial seeds
Xi;0 = 100, 300, 500, for the individual generators i = 1, 2, 3.
(b) Apply the uniformity and independence tests to the generator and comment on the
results.
5. Characteristics of Random Numbers
Test the following sequence of numbers for uniformity and independence.
0.594, 0.928, 0.515, 0.055, 0.507, 0.351, 0.262, 0.797, 0.788, 0.442, 0.097, 0.798, 0.227,
0.127, 0.474, 0.825, 0.007, 0.182, 0.929, 0.852
6. Characteristics of Random Numbers
In some applications, it is useful to be able to quickly skip ahead in a pseudo-random
number sequence without actually generating all of the intermediate values.
(a) For a linear congruential generator with c = 0, show that Xi+n = αnXi mod m.
(b) Show that (αnXi) mod m = (αn mod m)Xi mod m
(c) Use this result to compute X6 with a congruential generator with m = 100; α = 19,
and c = 0. Start with X0 = 63 and check your answer by computing X6 in the
usual way.
7. Random-Variate Generator
Develop a random-variate generator for a random variable X with the pdf

f(x) =	(1)
e-4x	-1 < x ≤0
e4x	0 < x < 1

8. Input Modeling The time required for the transmission of a message (in minutes) is
sampled electronically at a communications center. The last 50 values in the sample are
as follows.
7.936 4.612 2.407 4.278 5.132
4.599 5.224 2.003 1.857 2.696
5.259 7.563 3.937 6.908 5.002
6.212 2.759 7.172 6.513 3.326
8.761 4.502 6.188 2.566 5.515
3.785 3.742 4.682 4.346 5.359
3.535 5.061 4.629 5.298 6.492
3.502 4.266 3.129 1.298 3.454
5.289 6.805 3.827 3.912 2.969
4.646 5.963 3.829 4.402 4.924
(a) How are the transmission times distributed?
(b) Develop and test an appropriate model.
9. Input Modeling
The time (in minutes) between requests to a webserver was recorded with the following
last 50 requests.
0.661 4.910 8.989 12.801 20.249
5.124 15.033 58.091 1.543 3.624
13.509 5.745 0.651 0.965 62.146
15.512 2.758 17.602 6.675 11.209
2.731 6.892 16.713 5.692 6.636
2.420 2.984 10.613 3.827 10.244
6.255 27.969 12.107 4.636 7.093
6.892 13.243 12.711 3.411 7.897
12.413 2.169 0.921 1.900 0.315
4.370 0.377 9.063 1.875 0.790
(a) How are the transmission times distributed?
(b) Develop and test an appropriate model.
10. Evaluation of simulation models
For each of the systems described below, under what circumstances would it be appropriate to use a terminating simulation versus a steady-state simulation to analyze the
system?
(a) A walk-in medical clinic simulated to determine staffing levels.
(b) A portfolio of stocks, bonds, and derivate securities simulated to estimating the
long-run return.
(c) A path over a set of internet routers connecting two hosts A and B to estimate the
throughput.
(d) A large local area network (LAN) with n hosts and k switches in tree/star-topology
to estimate the throughput.
(e) The Internet to estimate the throughput of any pairs of source-destination.
11. Output data analysis
Why is determining the required number of tellers for a bank different from determining
the hardware requirements for a computer or communications systems?
12. Confidence interval
Construct a 95 percent confidence interval for µw = µx - µy given the following data.
X = f3.06, 2.79, 2.21, 2.54, 9.27, 3.09, 2.5, 0.31, 3.17, 0.98 g
Y = f3.81, 3.37, 2.61, 3.59, 11.02, 3.75, 2.84, 0.71, 3.94, 1.18 g
Let Wj = Xj - Yj and m = n = 10.
Is the confidence interval statistically significant?
GOOD LUCK!
13. (20 points) Reading
Choose Two journal papers from journals folder given to you.Discuss about the
problems in each paper and the findings of the authors.
What is themain point in each paper?