Foundation Design: Principles and Practices (3rd Edition)
3rd Edition
ISBN: 9780133411898
Author: Donald P. Coduto, William A. Kitch, Man-chu Ronald Yeung
Publisher: PEARSON
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Assume a car park facility where the arrival rate is λ customer every minute, and the service
process including pressing the button, taking the card, and waiting for the boom to rise leads
to service rate of μ customer every minute.
a. Assume the arrival and service processes are stochastic. Using any software (Excel, Matlab,
or the one you prefer), plot average delay time (including service time) and average queue
size (including the vehicle currently being served) for all combinations of λ = {1,2,3,..,10}
and p = {0.1,0.3,0.5,0.7,0.9}. Specifically, we ask you to make 2 graphs (one for average
delay and the other for average queue size), where the x-axes contains the different values
for 1, and where you make one curve for each p.
b. Assume the arrival process is stochastic but the service process is deterministic with rate µ.
Using any software (Excel, Matlab, or the one you prefer), plot average delay time (including
service time) and average queue size (including the vehicle…
Consider, M people (aka pax) who want to travel by car from O to D. They all start working at
D at Q (e.g., Q-8am). If a person departs at time t, assume the time needed to go from O to D
is given by c(t)=A+Bx(t), where x(t) is the flow of people departing at time t [car/unit of time].
In addition, a is the penalty for being early at work (E(t) is how early the person arrived when
departing at time t), and ẞ is the penalty for being late at work (L(t) is how late the person
arrived when departing at time t). Assume 0 < a < 1 < ß. Further assume the departure time
choice problem under the equilibrium conditions. Prove that the arrival time of people who
depart when most of the M people start their trips is equal to Q.
Consider, M people (aka pax) who want to travel by car from O to D. They all start working at
D at Q (e.g., Q=8am). If a person departs at time t, assume the time needed to go from O to D
is given by c(t)=A+Bx(t), where x(t) is the flow of people departing at time t [car/unit of time].
In addition, a is the penalty for being early at work (E(t) is how early the person arrived when
departing at time t), and ẞ is the penalty for being late at work (L(t) is how late the person
arrived when departing at time t). Assume 0 < a < 1 < ß. Further assume the departure time
choice problem under the equilibrium conditions. Prove that the arrival time of people who
depart when most of the M people start their trips is equal to Q.
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