Example 4: Consider a tour guide at Taj Mahal. Customers arrive to him in the form of groups. The group size and the arrival time are random variables, both following Poisson distribution with parameter 4 and 8 respectively. After giving them a tour of the place, the group leaves. The time taken to see the place is a random variable following exponential distribution with parameter 20. The group leaves together thereafter. Obtain the measures of effectiveness for the same. Solution: The stated problem can be modeled as a bulk arrival and bulk service model. The arrival of the customers is in groups, where the size of the group follows Poisson distribution with parameter 4. Service is also done in bulks. However, in this case, the entire batch is served whatever size the batch is. Considering this, we set the size of bulk service large enough so that an arriving batch, of any size (atmost the mentioned size), is served completely. The system is hence modeled as an M [ X ] / M / 1 . In order to obtain the measures of effectiveness, we follow the steps as shown below: ¾ Open the page where the experimentation is to be performed
¾ Feed the data as shown:
¾ Next, click on the ‘Start’ button to obtain the desired measures of effectiveness
¾ In the simulator we can choose the queuing discipline to be either FIFO, LIFO or Random
Example 5: Consider a shop to which customers arrive in batches of random size. The batch size and the arrival time are random variables, both following Poisson distribution with parameter 4 and 8 respectively. The shopkeeper serves the customer one at a time. The time to serve the customer is a random variable distributed exponentially with parameter 10. Model this as a bulk arrival queueing system and obtain the measures of effectiveness for the same. Solution: ¾ Open the page where the experimentation is to be performed ¾ Feed the data as shown: ¾ Next, click on the ‘Start’ button to obtain the desired measures of effectiveness
Example 6: Consider a laughing club to which the audience arrives at the rate of 8 audiences in a min. The club can accommodate atmost 10 customers. After the club is full, the audiences are entertained. The time for entertainment is a random variable following exponential distribution. The audiences are entertained for an average time of 30 minutes. Model this as a bulk service queueing system and obtain the measures of effectiveness for the same. Solution: ¾ Open the page where the experimentation is to be performed ¾ Feed the data as shown: ¾ Next, click on the ‘Start’ button to obtain the desired measures of effectiveness
Example 7: Consider a shop to which customers arrive in batches of random size. The batch size and the arrival time are random variables, both following Poisson distribution with parameter 4 and 8 respectively. The shopkeeper serves the customer one at a time. The time to serve the customer is a random variable distributed exponentially with parameter 10. A customer may choose for retrial if there are already many customers in the queue. A customer retries after a random time. The time for retrial is also exponentially distributed with parameter 20. Atmost 15 customers can retry. Model this as a bulk arrival retrial queueing system and obtain the measures of effectiveness for the same. Solution: ¾ Open the page where the experimentation is to be performed ¾ Feed the data as shown: ¾ Next, click on the ‘Start’ button to obtain the desired measures of effectiveness