COM 5320 Queueing Theory, Final ExaniinatiOn, Spring 2011
I) (5%) Show that Poisson arrivals implies exponential interanival times.
2) (5%) 'Prove that if X is exponentially distributed, then X is memoryless.
3) (5%) Draw the statetransition diagram for t
Fundamentals of Analytical Chemistry: 9th ed.
15-1. Not only is NaHA a proton donor, it is also the conjugate base of the parent acid H2A.
HA + H2O H3O+ + A2
HA + H2O H2A + OH
Solutions of acid salts can be acidic or alkaline, depend
Course Description: Seminar (Analytical Division) (CHEM567000 and 667000)
by Kui-Thong TAN
Oral presentation and interactive discussions on recent literatures in analytical
chemistry and related fields which have SCI IF of at least 5.
C855 31 Queueing Theory, Final Examination, Fall 2009
1) (10%) Show that Poisson arrivals implies exponential interarrival times.
2) (10%) Prove that if X is exponentially distributed, then X is memoryless.
3) (10%) Derive the state transition probabiliti
a. I L o' -'- "J -* i r x
_:_fr (E (L. f) cILEI'T if cfw_5165 J E/fm U 1; 1L q, i ll 1"ij
_ . - 4"; 7);.
T" (vi-(1', )"Eflil$3 / hid" .
U 2007 Fal Queueing Theory Fmal Exam (. . ,
w H r-_ . l ._ ; _J
K _ " _ hi._'.!_-j;='f"l)j;:ii T I I31; Ci
ins ti .
Queueing Theory, Final Examination, F 311 1995
1) onsider @T which M customers circulate around through two queueing facilities
Stay. 1 igiqag 1 _ 1
Both servers are of the exponential type with rates [11 and 112, respectively. Let
I p], =
Queueing Theory, Final Examination, Fall 1996
1) (10%) For an M/M/i queue with r nonpreemptive priorities, the mean waiting time for customers
with priority 2' is given by '
WM 2 iii
q (1 "Oi1X1 Uii
where pi. = - and 0;: 2 2m.
Find the mea
(385531 Queueing Theory, Final Examination, Fall 2008
1) Consider an M/M/l system with parameters A and ,u in which exactly r customers arrive at each arrival
(a) (5%) Draw the state-transitionrate diagram.
(b) (10%) By inspection, write clown th
2006 Fall Queueing Theory Final Solution
UO/Let T1 be the rst interarrival time of the Poisson process 1
Let T; be the 1st Enter-arrival time of the Poisson process 2
P1[T1 < T2] f0 PI'[T2 >T1IT1~t] le(t) tit:
3) pn. = #7171:
DO I 1: n
b) "201% =
Queueing Theory, Final Examination, Fall 2012
1) Consider an MIMIC queue with parameters A and n.
(a) (5%) What is the average number of customers in the service facility?
(b) (5%) What is the probability that a server is busy?
2) Consider an M/M/l queue