- Text
- Module,
- Arena,
- Entity,
- Attribute,
- Queue,
- Resource,
- Transporter,
- Entities,
- Specified,
- Simulation

A • STATISTICAL DISTRIBUTIONS The cumulative distribution function F(x) is piecewise linear with “corners” defined by F(x j ) = c j for j = 1, 2, . . ., n. Thus, for j > 2, the returned value will be in the interval (x j–1 , x j ] with probability c j – c j–1 ; given that it is in this interval, it will be distributed uniformly over it. You must take care to specify c 1 and x 1 to get the effect you want at the left edge of the distribution. The CONTINUOUS function will return (exactly) the value x 1 with probability c 1 . Thus, if you specify c 1 > 0, this actually results in a mixed discretecontinuous distribution returning (exactly) x 1 with probability c 1 , and with probability 1 – c 1 a continuous random variate on (x 1 , x n ] as described above. The graph of F(x) above depicts a situation where c 1 > 0. On the other hand, if you specify c 1 = 0, you will get a (truly) continuous distribution on [x 1 , x n ] as described above, with no “mass” of probability at x 1 ; in this case, the graph of F(x) would be continuous, with no jump at x 1 . As an example use of the CONTINUOUS function, suppose you have collected a set of data x 1 , x 2 , . . ., x n (assumed to be sorted into increasing order) on service times, for example. Rather than using a fitted theoretical distribution from the Input Analyzer, you want to generate service times in the simulation “directly” from the data, consistent with how they’re spread out and bunched up, and between the minimum x 1 and the maximum x n you observed. Assuming that you don’t want a “mass” of probability sitting directly on x 1 , you’d specify c 1 = 0 and then c j = (j – 1)/(n – 1) for j = 2, 3, . . ., n. Range [x 1 , x n ] Applications The continuous empirical distribution is often used to incorporate actual data for continuous random variables directly into the model. This distribution can be used as an alternative to a theoretical distribution that has been fitted to the data, such as in data that have a multimodal profile or where there are significant outliers. 155

GETTING STARTED WITH ARENA Discrete: DISCRETE(CumP 1 , Val 1 , . . ., CumP n , Val n ) (c 1 , x 1 , . . ., c n , x n ) Probability Mass Function p(x j ) = c j – c j-1 where c 0 = 0 Cumulative Distribution Function Parameters The DISCRETE function in Arena returns a sample from a user-defined discrete probability distribution. The distribution is defined by the set of n possible discrete values (denoted by x 1 , x 2 , . . . , x n ) that can be returned by the function and the cumulative probabilities (denoted by c 1 , c 2 , . . . , c n ) associated with these discrete values. The cumulative probability (c j ) for x j is defined as the probability of obtaining a value that is less than or equal to x j . Hence, c j is equal to the sum of p(x k ) for k going from 1 to j. By definition, c n = 1. Range {x 1 , x 2 , . . ., x n } 156

- Page 1 and 2:
Arena ® USER’S GUIDE PUBLICATION

- Page 3 and 4:
ii

- Page 5 and 6:
GETTING STARTED WITH ARENA View sim

- Page 7 and 8:
GETTING STARTED WITH ARENA Network

- Page 10 and 11:
1 Welcome What is Arena software? A

- Page 12 and 13:
1 • WELCOME Arena Help); text you

- Page 14:
1 • WELCOME ten attendees. You de

- Page 17 and 18:
GETTING STARTED WITH ARENA The Aren

- Page 19 and 20:
GETTING STARTED WITH ARENA Every pr

- Page 21 and 22:
GETTING STARTED WITH ARENA Decide w

- Page 23 and 24:
GETTING STARTED WITH ARENA Define m

- Page 25 and 26:
GETTING STARTED WITH ARENA If more

- Page 27 and 28:
GETTING STARTED WITH ARENA 3. For t

- Page 29 and 30:
GETTING STARTED WITH ARENA 2. Becau

- Page 31 and 32:
GETTING STARTED WITH ARENA The anim

- Page 33 and 34:
GETTING STARTED WITH ARENA you coul

- Page 35 and 36:
GETTING STARTED WITH ARENA Animate

- Page 37 and 38:
GETTING STARTED WITH ARENA You can

- Page 39 and 40:
GETTING STARTED WITH ARENA Next ste

- Page 41 and 42:
GETTING STARTED WITH ARENA Prompt V

- Page 43 and 44:
GETTING STARTED WITH ARENA Prompt A

- Page 45 and 46:
GETTING STARTED WITH ARENA Prompt S

- Page 47 and 48:
GETTING STARTED WITH ARENA Batch mo

- Page 49 and 50:
GETTING STARTED WITH ARENA Prompt M

- Page 51 and 52:
GETTING STARTED WITH ARENA PROMPTS

- Page 53 and 54:
GETTING STARTED WITH ARENA PROMPTS

- Page 55 and 56:
GETTING STARTED WITH ARENA PROMPTS

- Page 57 and 58:
GETTING STARTED WITH ARENA Prompt I

- Page 59 and 60:
GETTING STARTED WITH ARENA Prompt F

- Page 61 and 62:
GETTING STARTED WITH ARENA PROMPTS

- Page 63 and 64:
GETTING STARTED WITH ARENA Dropoff

- Page 65 and 66:
GETTING STARTED WITH ARENA Prompt S

- Page 67 and 68:
GETTING STARTED WITH ARENA ReadWrit

- Page 69 and 70:
GETTING STARTED WITH ARENA Prompt V

- Page 71 and 72:
GETTING STARTED WITH ARENA PROMPTS

- Page 73 and 74:
GETTING STARTED WITH ARENA Prompt S

- Page 75 and 76:
GETTING STARTED WITH ARENA Store mo

- Page 77 and 78:
GETTING STARTED WITH ARENA When an

- Page 79 and 80:
GETTING STARTED WITH ARENA Expressi

- Page 81 and 82:
GETTING STARTED WITH ARENA Prompt U

- Page 83 and 84:
GETTING STARTED WITH ARENA TYPICAL

- Page 85 and 86:
GETTING STARTED WITH ARENA Prompt C

- Page 87 and 88:
GETTING STARTED WITH ARENA Prompt V

- Page 89 and 90:
GETTING STARTED WITH ARENA Prompt D

- Page 91 and 92:
GETTING STARTED WITH ARENA referenc

- Page 93 and 94:
GETTING STARTED WITH ARENA Prompt E

- Page 95 and 96:
GETTING STARTED WITH ARENA When an

- Page 97 and 98:
GETTING STARTED WITH ARENA Prompt R

- Page 99 and 100:
GETTING STARTED WITH ARENA Prompt D

- Page 101 and 102:
GETTING STARTED WITH ARENA PROMPTS

- Page 103 and 104:
GETTING STARTED WITH ARENA Prompt Q

- Page 105 and 106:
GETTING STARTED WITH ARENA TYPICAL

- Page 107 and 108:
GETTING STARTED WITH ARENA Prompt Q

- Page 109 and 110:
GETTING STARTED WITH ARENA Prompt E

- Page 111 and 112:
GETTING STARTED WITH ARENA Prompt S

- Page 113 and 114:
GETTING STARTED WITH ARENA Transpor

- Page 115 and 116: GETTING STARTED WITH ARENA Prompt S
- Page 117 and 118: GETTING STARTED WITH ARENA Prompt D
- Page 119 and 120: GETTING STARTED WITH ARENA and/or P
- Page 121 and 122: GETTING STARTED WITH ARENA Prompt D
- Page 123 and 124: GETTING STARTED WITH ARENA Prompt D
- Page 125 and 126: GETTING STARTED WITH ARENA PROMPTS
- Page 127 and 128: GETTING STARTED WITH ARENA Data mod
- Page 129 and 130: GETTING STARTED WITH ARENA Visual D
- Page 131 and 132: GETTING STARTED WITH ARENA Scene wi
- Page 133 and 134: GETTING STARTED WITH ARENA Style Cl
- Page 135 and 136: GETTING STARTED WITH ARENA Task Lis
- Page 137 and 138: GETTING STARTED WITH ARENA Bar cont
- Page 139 and 140: GETTING STARTED WITH ARENA The Anim
- Page 141 and 142: GETTING STARTED WITH ARENA Since we
- Page 143 and 144: GETTING STARTED WITH ARENA To run a
- Page 145 and 146: GETTING STARTED WITH ARENA and any
- Page 147 and 148: GETTING STARTED WITH ARENA Working
- Page 149 and 150: GETTING STARTED WITH ARENA 4. In th
- Page 151 and 152: GETTING STARTED WITH ARENA . Use th
- Page 153 and 154: GETTING STARTED WITH ARENA 10. With
- Page 155 and 156: GETTING STARTED WITH ARENA 14. In t
- Page 157 and 158: GETTING STARTED WITH ARENA ANIMATIN
- Page 159 and 160: system automatically appends the na
- Page 161 and 162: GETTING STARTED WITH ARENA 152
- Page 163 and 164: GETTING STARTED WITH ARENA To enter
- Page 165: GETTING STARTED WITH ARENA Continuo
- Page 169 and 170: GETTING STARTED WITH ARENA Erlang(,
- Page 171 and 172: GETTING STARTED WITH ARENA Gamma(,
- Page 173 and 174: GETTING STARTED WITH ARENA Lognorma
- Page 175 and 176: GETTING STARTED WITH ARENA Poisson(
- Page 177 and 178: GETTING STARTED WITH ARENA Uniform(
- Page 179 and 180: GETTING STARTED WITH ARENA Applicat
- Page 181 and 182: GETTING STARTED WITH ARENA Arena .p
- Page 184 and 185: B • LIBRARY SHAPES AND SYMBOLS 17
- Page 186 and 187: B • LIBRARY SHAPES AND SYMBOLS 17
- Page 188 and 189: B • LIBRARY SHAPES AND SYMBOLS 17
- Page 190 and 191: GETTING STARTED WITH ARENA The Visi
- Page 192 and 193: GETTING STARTED WITH ARENA Connecto
- Page 194 and 195: GETTING STARTED WITH ARENA You only
- Page 196 and 197: GETTING STARTED WITH ARENA Transfer
- Page 199 and 200: Index Numerics 2-way chance • 36
- Page 201 and 202: INDEX on conveyors • 88 releasing
- Page 203: INDEX Tank module • 109 Task List