Google Answers Logo
View Question
 
Q: modelling and simulation Bank Teller System Single Queue Single Server System ( No Answer,   0 Comments )
Question  
Subject: modelling and simulation Bank Teller System Single Queue Single Server System
Category: Computers > Algorithms
Asked by: pushtak-ga
List Price: $25.00
Posted: 17 Sep 2005 06:48 PDT
Expires: 25 Sep 2005 07:42 PDT
Question ID: 569075
Note: Spread sheet is pasted at bottom, If you need attchment file,
pls send me ur email ID
Question:Consider the operation of a bank that has a separate waiting
line in front of each teller?s window. In this situation each window
can be considered a Single Queue Single Server System. Suppose that
both interarrival and service times are exponentially distributed.

a)Create a spreadsheet to simulate the operation of the bank teller
for 25 customers (a Single Queue Single Server system). Assume that
the mean values of the interarrival and service times are 4 and 3
minutes, respectively. Choose the seed values Z1
 equal to the last digit of your College ID #, (if it is 
     zero, then select  Z1=6) and Z2
     equal to the last three digits of your College ID #. 
   It will display the following information:

 Stream 1 Random Number	Interarrival Time Stream 2 Random Number
Service Time	Customer Number	Arrival Time	Idle Time for Teller	Begin
Service Time	Service Time	Departure Time	Time in Queue	Time in System
i	Z1i 	U1i	X1i	Z2i	U2i	X2i	 	 	 	 	 	 	 	 


and 

the average waiting time for a customer=(total time customers wait in
queue)/(total number of customers)

the probability that a customer has to wait in the queue=
                               =(# of customers who wait)/(total
number of customers)

the probability that server is idle=
           =(total idle time of server)/(total run time of simulation)
Note that total run time of simulation=departure time of last customer

the average service time =(total service time)/(total number of customers)

the average waiting time of those who wait=(total time customers wait
in queue)/(total number of customers who wait)

the average time that a customer spends in the bank= 
         =total time customers spend  in the bank)/ ( total number of customers)

the average time between arrivals(interarrival time)=
      =(sum of all times between arrivals)/(# of arrivals-1)
Note that sum of all times between arrivals= arrival time of last customer
and  # of arrivals= total number of customers.


b)Investigate the effect of the interarrival and service times on the
bank teller system by repeating the part (a) for different
interarrival and service times. Create a summary table and make
comments on the findings.
c)Repeat the simulation of the operation of the bank teller for 10
    times by changing the seed values and . Calculate the average of 
     the average of Idle Time for Teller,
     the average Time in Queue and
     the average Time in System. 
     Create a summary table and make comments on the findings.

  Spread sheet:
    	
Stream 1	Random Number	Interarrival Time	Stream 2	Random
Number	Service Time	Customer Number	Arrival Time	Idle Time for
Teller	Begin Service Time	Service Time	Departure Time	Time in
Queue	Time in System
i	Z1i 	U1i	X1i	Z2i	U2i	X2i	1	2	3	4	5	6=4+5	7=4-2	8=6-2
0	3			122										
1	66	0.516	2.17	5	0.039	0.10	1	2.17	2.17	2.17	0.10	2.27	0.00	0.10
2	109	0.852	5.72	108	0.844	4.46	2	7.90	5.63	7.90	4.46	12.35	0.00	4.46
3	116	0.906	7.10	95	0.742	3.25	3	15.00	2.65	15.00	3.25	18.25	0.00	3.25
4	7	0.055	0.17	78	0.609	2.26	4	15.17	0.00	18.25	2.26	20.51	3.08	5.34
5	22	0.172	0.57	105	0.820	4.12	5	15.73	0.00	20.51	4.12	24.63	4.77	8.89
6	81	0.633	3.01	32	0.250	0.69	6	18.74	0.00	24.63	0.69	25.32	5.89	6.58
7	40	0.313	1.12	35	0.273	0.77	7	19.86	0.00	25.32	0.77	26.08	5.46	6.22
8	75	0.586	2.65	98	0.766	3.48	8	22.51	0.00	26.08	3.48	29.57	3.58	7.06
9	42	0.328	1.19	13	0.102	0.26	9	23.70	0.00	29.57	0.26	29.82	5.87	6.12
10	117	0.914	7.36	20	0.156	0.41	10	31.06	1.24	31.06	0.41	31.47	0.00	0.41
11	28	0.219	0.74	39	0.305	0.87	11	31.80	0.33	31.80	0.87	32.68	0.00	0.87
12	79	0.617	2.88	54	0.422	1.32	12	34.68	2.01	34.68	1.32	36.00	0.00	1.32
13	126	0.984	12.48	113	0.883	5.15	13	47.16	11.16	47.16	5.15	52.31	0.00	5.15
14	89	0.695	3.57	72	0.563	1.98	14	50.73	0.00	52.31	1.98	54.29	1.58	3.56
15	80	0.625	2.94	107	0.836	4.34	15	53.67	0.00	54.29	4.34	58.63	0.62	4.96
16	19	0.148	0.48	74	0.578	2.07	16	54.15	0.00	58.63	2.07	60.70	4.48	6.55
17	18	0.141	0.45	21	0.164	0.43	17	54.61	0.00	60.70	0.43	61.13	6.09	6.52
18	125	0.977	11.26	60	0.469	1.52	18	65.87	4.74	65.87	1.52	67.38	0.00	1.52
19	68	0.531	2.27	111	0.867	4.85	19	68.14	0.76	68.14	4.85	72.98	0.00	4.85
20	23	0.180	0.59	30	0.234	0.64	20	68.73	0.00	72.98	0.64	73.63	4.25	4.89
21	102	0.797	4.78	121	0.945	6.97	21	73.52	0.00	73.63	6.97	80.60	0.11	7.08
22	97	0.758	4.25	112	0.875	4.99	22	77.77	0.00	80.60	4.99	85.59	2.83	7.82
23	120	0.938	8.32	51	0.398	1.22	23	86.09	0.50	86.09	1.22	87.31	0.00	1.22
24	91	0.711	3.72	50	0.391	1.19	24	89.81	2.50	89.81	1.19	91.00	0.00	1.19
25	122	0.953	9.18	29	0.227	0.62	25	98.99	7.99	98.99	0.62	99.61	0.00	0.62
							Average		1.67				1.94	4.26

Clarification of Question by pushtak-ga on 17 Sep 2005 06:51 PDT
I need answer by Monday 09/19/05 Noon
Answer  
There is no answer at this time.

Comments  
There are no comments at this time.

Important Disclaimer: Answers and comments provided on Google Answers are general information, and are not intended to substitute for informed professional medical, psychiatric, psychological, tax, legal, investment, accounting, or other professional advice. Google does not endorse, and expressly disclaims liability for any product, manufacturer, distributor, service or service provider mentioned or any opinion expressed in answers or comments. Please read carefully the Google Answers Terms of Service.

If you feel that you have found inappropriate content, please let us know by emailing us at answers-support@google.com with the question ID listed above. Thank you.
Search Google Answers for
Google Answers  


Google Home - Answers FAQ - Terms of Service - Privacy Policy