Week10 practice 1 - ประวัติรุ่นแก้ไข

Jittat: /* Simulation with exponential random variables */

2014-10-28T03:17:48Z

Simulation with exponential random variables

Jittat: /* Simulation with exponential random variables */

2014-10-28T03:16:43Z

Simulation with exponential random variables

Jittat เมื่อ 02:55, 28 ตุลาคม 2557

2014-10-28T02:55:54Z

Jittat: /* Simulations */

2014-10-28T02:53:23Z

Simulations

Jittat: /* Simulation with Poisson random variables */

2014-10-28T02:49:34Z

Simulation with Poisson random variables

Jittat: /* Simulation with Poisson random variables */

2014-10-28T02:48:38Z

Simulation with Poisson random variables

Jittat: /* Simulation with Poisson random variables */

2014-10-28T02:47:35Z

Simulation with Poisson random variables

Jittat: /* Simulations */

2014-10-28T02:47:06Z

Simulations

Jittat: /* Simulation with Poisson random variables */

2014-10-28T02:46:15Z

Simulation with Poisson random variables

Jittat: /* Simulations */

2014-10-28T02:33:33Z

Simulations

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 03:17, 28 ตุลาคม 2557
แถว 126:		แถว 126:

	You can measure the average wait time (average of 0, 0, (0.665 - 0.618), (0.865 - 0.789), 0, (1.276 - 1.158)), and the maximum wait time for all customers (0.118 = 1.276 - 1.158).		You can measure the average wait time (average of 0, 0, (0.665 - 0.618), (0.865 - 0.789), 0, (1.276 - 1.158)), and the maximum wait time for all customers (0.118 = 1.276 - 1.158).
		+
		+	'''Optional:''' For average queue size and max queue size, you will have to use more accurate simulation mechanism, i.e., you may have to actually maintain a queue.

	== Relationships ==		== Relationships ==

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 03:16, 28 ตุลาคม 2557
แถว 107:		แถว 107:

	=== Simulation with exponential random variables ===		=== Simulation with exponential random variables ===
		+	Exponential random variables model the "wait" period between events. Suppose that we consider having customers arriving at rate <math>\lambda = 4</math> customers per minute. Generating an exponential r.v. with parameter <math>\lambda=4</math>, you get:
		+
		+	* 0.047, 0.418, 0.153, 0.171, 0.287, 0.082, ...
		+
		+	These are periods between two customers. From that, we have that customers arrive at time
		+
		+	* 0.047, 0.465, 0.618, 0.789, 1.076, 1.158, ...
		+
		+	Since our server can deliver 5 dishes per minute, the server takes 0.2 minutes to complete any request. Using the above arriving times, we can run our simulation like this:
		+
		+	* Customer 1, arriving at 0.047: server is free, get served at 0.047, done at 0.047 + 0.2 = 0.247
		+	* Customer 2, arriving at 0.465: server is free, get served at 0.465, done at 0.465 + 0.2 = 0.665
		+	* Customer 3, arriving at 0.618: server is not free (free at 0.665), get served at 0.665, done at 0.665 + 0.2 = 0.865
		+	* Customer 4, arriving at 0.789: server is not free (free at 0.865), get served at 0.865, done at 0.865 + 0.2 = 1.065
		+	* Customer 5, arriving at 1.076: server is free (because 1.065 < 1.076), get served at 1.076, done at 1.076 + 0.2 = 1.276
		+	* Customer 6, arriving at 1.158: server is not free (free at 1.276), get served at 1.276, done at 1.276 + 0.2 = 1.476
		+	* and so on ...
		+
		+	You can measure the average wait time (average of 0, 0, (0.665 - 0.618), (0.865 - 0.789), 0, (1.276 - 1.158)), and the maximum wait time for all customers (0.118 = 1.276 - 1.158).

	== Relationships ==		== Relationships ==

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:55, 28 ตุลาคม 2557
แถว 1:		แถว 1:
		+	: ''This is part of [[probstat]].''
		+
	== Generating Poisson and exponential random variables ==		== Generating Poisson and exponential random variables ==

@@ แถว 72: / แถว 72: @@
 * maximum queue size over time,
-when customers come in at the rate of 2, 3, 4.5, 4.8, 4.9, 5, 5.1, 5.5, 6, and 7 customers per minute.
+when customers come in at the specified rates.
 === Simulation with Poisson random variables ===

@@ แถว 88: / แถว 88: @@
 |-
 ! minute
-| 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8
+| 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || ...
 |-
 ! new customers
-| 3 || 4 || 7 || 4 || 5 || 6 || 2 || 5
+| 3 || 4 || 7 || 4 || 5 || 6 || 2 || 5 || ...
 |-
 ! queue size (beginning)
-| 3 || 4 || 7 || 6 || 6 || 7 || 4 || 5
+| 3 || 4 || 7 || 6 || 6 || 7 || 4 || 5 || ...
 |-
 ! queue size (end)
-| 0 || 0 || 2 || 1 || 1 || 2 || 0 || 0
+| 0 || 0 || 2 || 1 || 1 || 2 || 0 || 0 || ...
 |}
-In this case, the average queue size is (3+4+7+6+6+7+4+5)/8 = 5.25, and the max queue size is 7.
+In this case, the average queue size (up to the values shown in the table) is (3+4+7+6+6+7+4+5)/8 = 5.25, and the max queue size is 7.
 === Simulation with exponential random variables ===
 == Relationships ==

@@ แถว 79: / แถว 79: @@
 For example, when <math>\lambda = 4</math>, you might get the following sequence
-* 3, 4, 7, 3, 5, 6, 2, 5, 4, 7, ...
+* 3, 4, 7, 4, 5, 6, 2, 5, 4, 7, ...
 You can generate 10,000 of these random numbers.  Then you can feed it in a simulator that acts like a server.   For each minute, it serves 5 customers in the queue.  The number of customer in a queue is a given minute is the number remaining from the last minute plus the number arriving at this minute.  If the number of customers is at most 5, all of them is gone in the next minute; otherwise, there will be some unserved customer and they will be in the queue for the next minute.
@@ แถว 91: / แถว 91: @@
 |-
 ! new customers
-| 3 || 4 || 7 || 3 || 5 || 6 || 2 || 5
+| 3 || 4 || 7 || 4 || 5 || 6 || 2 || 5
 |-
 ! queue size (beginning)
-| 3 || 4 || 7 || 5 || 5 || 6 || 3 || 5
+| 3 || 4 || 7 || 6 || 5 || 7 || 4 || 5
 |-
 ! queue size (end)
-| 0 || 0 || 2 || 0 || 0 || 1 || 0 || 0
+| 0 || 0 || 2 || 1 || 1 || 2 || 0 || 0
 |}

←รุ่นแก้ไขก่อนหน้า		รุ่นแก้ไขเมื่อ 02:33, 28 ตุลาคม 2557
แถว 73:		แถว 73:

	when customers come in at the rate of 2, 3, 4.5, 4.8, 4.9, 5, 5.1, 5.5, 6, and 7 customers per minute.		when customers come in at the rate of 2, 3, 4.5, 4.8, 4.9, 5, 5.1, 5.5, 6, and 7 customers per minute.
		+
		+	=== Simulation with Poisson random variables ===
		+
		+	=== Simulation with exponential random variables ===

	== Relationships ==		== Relationships ==