{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw9soln - 112:3 a A parking lot is a queueing system for...

This preview shows pages 1–12. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 112:3 a) A parking lot is a queueing system for providing parking with cars as the customers, and parking spaces as the servers. The service time is the amount of time a car spends in a space. The queue capacity is O. b) L = 0(Po)+1(P,)+ 2(PZ) + 3(P3) = 0(0.2) + l(0.3) + 2(0.3) + 3(0.2) = 1.5 cars Lq = 0 cars W = (E) = (E) = 0.75 hours ft 2 L W] = [—f) = (-29) = 0 hours c) A car spends an average of 45 minutes in a parking space. 11‘4'5 85 mow/e59 7’»qu , U = min/7“,, 7;, 7;) T, ~exP(%.o), ,71~exf('/;) , T; ~exﬂ I//o) vweXf(-L-+,—’~+7g-)= «ff—6%) 3°. WM war/757 17kt = 7% = 4‘8 Inf/”0755 /3 b) w=wﬁ+72 , up.“ an/Mw Eu): 805+ E]? = 5m; =15 01;th = 2L 4,“, WW]: VMMﬁﬁ ”’7; =(7—li)z+ {ff—wi— =0.0547 0“ (,5: 51-005 (1:) KMWVI 2° ”I‘M. [MT Maloiﬁzem wank/,2 cult); /¢«§ (9 =9 PL=(6-§P.~2p.)/ = E’P. as P5=5§W5Po '§Po=P~ @ =? P;=(2P°-2 -JP°)/ = 314% mu ML D: P Hurts” ’7“ LA; ___( P WWV" n kilw 14:6-5 3:3,»:11’ \$;‘ ’ Pa3/l, The, sgstem wctkout the storage mstrccﬁon £5 a M/MH “Wen-IF ‘A square cast 0? Fkoor space we“2 QVacLablc ﬁr wactcmﬁvxiproporh‘ox oF hime £th WOuLd be suFRc‘Ceht CS 33‘1"“ we, wamt to 43an ”At suck that :22- >/ %C For 8,4,3"), 'wkere \$1:.5I%Aﬂ.q’%§.qq‘ 4 4 . Now ER 2% (=> 3 (1-p)p‘ >, %¢¢‘>("P) (1.2%”); w an L:0 (l—p) ‘(1 'n .1 (=5) 1~P U 3 (k (a P'nvzs 4-%e<¢(7\t+a)tnp5£n(1_%cy aunt”); EMU—311\$) ’"c 2 C (1-3 1 ”1 4 L: i=i=3 customers 11—). 40-30 W=—l—-=—1———=O.1hours 11—1 40—30 2. 30 W" = -————- = ————- = 0.075 hours ,u(,u — 1) 40(40 - 30) L4 = AW" = 30(0.075) = 2.25 customers P0 =l—p=1—O.75=O.25 P, = (1 — p)p = (1 - 0.75)0.75 = 0.188 P2 = (1 — p)p2 = (1 —0.75)0.752 = 0.141 There is a 42% chance of having more than 2 customers at the checkout stand. b) Data Results 30 (mean arrival rate) 40 (mean service rate) (# servers) PO+P1+P2= 0.578125 Igl-lf 116—9 6) 30 J_ .— ,u—x'L 60—30 W=;=_1__ 11—1 60—30 W 2:__4_______3_9_._ ' ”(11— A) 60(60—30) Ll] = qu = 30(0.075) = 0.5 customer P0 =1—p=1-0.5=O.5 1DI = (1 — p)p = (1 — 0.5)0.5 = 0.25 P2 = (1 -p)p2 = (1 —0.5)0.52 =0.125 L = = 1 customer = 0.033 hours = 0.017 hours There is a 12.5% chance of having more than 2 customers at the checkout stand. 30 (mean arrival rate) (mean service rate) (# servers) P0+P1+P2= 0.875 e) The manager should adopt the new approach of adding another person to bag the groceries. I746 Data Results 1 0 (mean arrival rate) 20 (mean service rate) (# servers) 0.0067379 0.5 P0+P1+P2+P3+P4+P5= 0.984375 All the criteria are currently being satisﬁed. b) Data Results (mean arrival rate) (mean service rate) (# servers) PO+P1+P2+P3+P4+P5= 0.822021484 None of the criteria are now satisﬁed. l7-l? (mean arrival rate) (mean service rate) (# servers) P0+P1+P2+P3+P4+P5= 0.926640437 In this case, the ﬁrst and third criteria are satisfied but the second is not. Data 116-15 (mean arrival rate) (mean service rate) (4 servers) “ , 9493125., 2.061E-09 when l = 10 Prob( ﬂu") =_ ' '«r-ul wwwuv. . °-§§§.3..333. 0 when t = 0.305555556 P0+P1= Data (mean arrival rate) (mean service rate) (# servers) f’.’°b‘.‘fa?.’)‘ 0245098 0 when t = 0897875817 P0+P1+P2= mean arrival rate) (mean service rate) (# servers) Pr(o)>t) = 8.047E-53 when t = 10 0.0577101 0 Prob( 0).») = when l = 0983969426 P0+P1+P2+P3= Data (mean arrival rate) (mean serwce rate) (# servers) . PM?!) -. 7.297553 when t = 10 Prob( n31): 6.0139241 .. ”ea-‘2 shy-www.- gm 0 when t = P0+P1+P2+P3+P4= 0997703314 17-20 I :°¥.1.388§§°9" ‘- -‘-"2’"...19:1j1.5740,74 ' ‘Pa "= 0.09645062- ._;,_:... 2259; r"— ~:m.x~&‘." Results Ls, 1100840336 ‘Laf' 9‘ 7597003 ' . P' " 6.1931572: P2 =. . 034297336 P= ;..9.0§9572.44 Results L = 0.85552951 0.02219618 008555295 000221962 . 027777778 .043213296 ' . 9.9601105 ' 045904617 (om/rib) 95 ‘~‘ 000271151 (couf'o) Data P0+P1+P2+P3+P4+P5= (mean arrival rate) (mean service rate) (# servers) 0.999708926 a) 2 servers b) 3 servers C) 2 servers d) Iserver e) 5 servers f) Iserver g) 3 servers ...
View Full Document

{[ snackBarMessage ]}