Copy of Queue Calculator

8/19/2019 Copy of Queue Calculator

1/12

models

Page 1

How to choose a queueing model

All models in this workbook are Poisson arrivals, infinite population, and FCFS.

The models differ by

(1 the servi!e time distribution (e"ponential, !onstant or #eneral

($ the number of servers (sin#le server or multiple servers

(% waitin# room !apa!ity (unlimited waitin# room or limited waitin# room buffer

M/M/1 M/D/1 M/G/1 M/M/s

Service time distribution Exponential Constant General Exponential

Number of servers Single Single Single Multiple

Waiting room capacity Unlimited Unlimited Unlimited Unlimited

The &rlan# 'oss odel is a spe!ial !ase of ))s)b model where the waitin# room !apa!ity (b is *ero.

The followin# models assume e"ponential distribution of servi!e time+

))1, ))s, ))s)bThe followin# models assume !onstant servi!e time+

)C)1

The followin# models assume #enerally distributed (su!h as normal servi!e time+

))1

The followin# models assume a sin#le server+

))1, )C)1, ))1

The followin# models assume multiple servers+

))s, ))s)b

The followin# models assume unlimited waitin# room !apa!ity+

))1, )C)1, ))1, ))sThe followin# models assume limited waitin# room !apa!ity+

))s)b


2/12

models

Page

M/M/s/b

Exponential

Multiple

!imited


3/12

M"M"1

Page #

odel 1 ())1 -ueue+

ellow !ells need user inputed values

Inputs/nits of time hour

Arrival rate (lambda 0.11 !usomters per

Servi!e rate (mu 0.0 !usomters per

OutputsDirect outputs from inputs

ean time between arrivals 2.000 hour

ean time per servi!e $ hour

Traffi! intensity (ro 0.$$$$$$$$$$

Summary measures

/tili*ation rate of server $$.$3

Avera#e number of !ustomers waitin# in line ('4 0.05%62$05% !ustomers

Avera#e number of !ustomers in system (' 0.$7816$78 !ustomers Avera#e time waitin# in line (94 0.816$7816 hour

Avera#e time in system (9 $.816$7816 hour

Probability of no !ustomers in system (P0 88.73 (this is the proba

:istribution of number of !ustomers in system

n (!ustomers P(n in system

0 0.888887

1 0.18$760

$ 0.0%7602

% 0.007%

:istribution of time in 4ueuet (time in 4ueue P(wait ; t

0.$ 0.$015%6

Sin#le server,


4/12

M"M"1

Page $

hour

hour

%6.$7816$78

16.$7816$78

ility of empty system

d 4ueue len#th


5/12

M"%"1

Page &

odel $ ()C)1 -ueue+


Inputs

unit of time minutes

Arrival rate (lambda 15 !ustomers per Servi!e rate (mu $0 !ustomers per


ean time between arrivals 0.05% minutes

&"a!t time per servi!e (no variability 0.0 minutes

Traffi! intensity 0.7

Summary measures

/tili*ation rate of server 70.03

Avera#e number of !ustomers waitin# in line ('4 1.5 !ustomers

Avera#e number of !ustomers in system (' $.6 !ustomers Avera#e time waitin# in line (94 0.1 minutes

Avera#e time in system (9 0.1 minutes

Probability of no !ustomers in system (P0 $0.03

Sin#le server,


6/12

M"%"1

Page '

minutesminutes

5

2

-ueue 'en#th


7/12

M"G"1

Page (

odel % ())1 -ueue+


Inputs

/nit of time minute

Arrival rate (lambda 0.5 !ustomers per Avera#e servi!e rate (mu 1.$ !ustomers per

Servi!e time standard deviation 0.% minute


ean time between arrivals 1.558 minute

ean time per servi!e 0.7%%%%%%%%% minute

Traffi! intensity 0.

Summary measures

/tili*ation rate of server 0.03

Avera#e number of !ustomers waitin# in line ('4 0.60555 !ustomers

Avera#e number of !ustomers in system (' 0.20555 !ustomers

Avera#e time waitin# in line (94 0.58885 minute

Avera#e time in system (9 1.1102%%%%% minute

Probability of no !ustomers in system (P0 0.03

Sin#le server,


8/12

M"G"1

Page )

minuteminute

ueue 'en#th


9/12

Model $* Multiple servers +it, in-nite +aiting room

odel 6 ())s -ueue+

ultiple servers,


10/12

Model &* Multiple servers +it, -nite bu.ers

odel ())s)b 4ueue+


Inputs $.

/nit of time hour

Arrival rate (lambda 10 !ustomers per hour

Servi!e rate (mu 6 !ustomers per hour

=umber of identi!al servers (s $ servers

@uffer (waitin# room si*e 10 !ustomers (The ma"imum number in system is e4ua

Outputs

Direct outputs from inputsean time between arrivals 0.100 hour

ean time per servi!e 0.$ hour

Traffi! intensity 1.$

Summary measures

Avera#e utili*ation rate of servers 27.63

Avera#e number of !ustomers waitin# in line ('4 5.7%6 !ustomers

Avera#e number of !ustomers in system (' 7.7$06 !ustomers

Avera#e time waitin# in line (94 0.7810 hour

Avera#e time in system (9 1.1$10 hour

Probability of no !ustomers in system (P0 0.008% (Probability of empty system

Probability of ree!tin# a !ustomer (balkin# rate $1.%$3 (Bee!t rate

&ffe!tive arrival rate 8.75710%582 (&nterin# rate

ultiple servers,


11/12

odel 1 ())1 -ueue+


Inputs/nits of time hour

Arrival rate (lambda 0.11 !usomters per

Servi!e rate (mu 0.0 !usomters per

= (umlah input yan# tersedia %.00 yaitu mesin

n 0 1.00

n 1 0.58

n $ 0.%0

n % 0.08

po 0.62

p1 0.%%

p$ 0.1

p% 0.0%

'4 0.$1

n 1 0.00n $ 0.1

n % 0.05

' 0.8171


ean time between arrivals 2.000 hour

ean time per servi!e $ hour

Traffi! intensity (ro 0.$$$$$$$$$$

Summary measures

/tili*ation rate of server $$.$3 Avera#e number of !ustomers waitin# in line ('4 0.05%62$05% !ustomers

Avera#e number of !ustomers in system (' 0.$7816$78 !ustomers

Avera#e time waitin# in line (94 0.816$7816 hour

Avera#e time in system (9 $.816$7816 hour

Probability of no !ustomers in system (P0 88.73 (this is the proba

:istribution of number of !ustomers in system

n (!ustomers P(n in system

0 0.888887

1 0.18$760

$ 0.0%7602

% 0.007%

:istribution of time in 4ueue

t (time in 4ueue P(wait ; t

0.$ 0.$015%6

Sin#le server, finite population, Poisson arrivals, FCFS, Exponential service time, /nlimited


12/12

hour

hour

0 1 $ %

%6.$7816$78

16.$7816$78

ility of empty system

4ueue len#th

Copy of Queue Calculator

Documents

Transcript of Copy of Queue Calculator