1. Customers arrive randomly at the \"Snips, Snails, & Puppy Dog Tails\" pet car
ID: 365621 • Letter: 1
Question
1. Customers arrive randomly at the "Snips, Snails, & Puppy Dog Tails" pet care shop, which operates in a manner consistent with the Model A queuing formulas. The average customer arrival rate is 10 per hour ( = 10). When the shop is busy, it can serve an average of 12 customers per hour ( = 12). For each of the following, state the name of the proper formula (Ls, Wq, etc.), and find the answer to 3 decimal placesshowing work: a. Average length of time in minutes that a customer waits until it is his or her turn. b. Average length of time in minutes that a customer spends in the shop (waiting and being served). c. Average number of customers waiting for service, not counting the customer currently being served if any. d. Average number of customers in the shop, counting the customer currently being served if any. e. Average percentage of the day that the shop has no customers. f. (Bonus: +1) The shop has just three parking places for customers. When they are filled, customers have to park at parking meters on the street. If each customer comes in a separate vehicle, what percentage of the day does at least one customer have to park on the street? Tips: Use the Model A formulas, and be careful about identifying which formula to use for each part. Answer questions that require minutes by first calculating the answer in hours, then converting.
Explanation / Answer
The City is in the process of installing enhanced traffic control equipment at the City's parking structures. The new equipment, which creates a more reliable parking experience, will be in place at all City parking structures by early June.
The system requires drivers to use a credit/debit card or IN Card (a card that can be loaded with various amounts) to pay for parking. IN Cards are available at the SP+ Parking Office at the Chester Street Parking Structure, and are now available at the Treasurer's Office in City Hall. The IN CARD can be purchased for $10.00, and then loaded with amounts of $25, $50, $100, or $200. The IN CARD can also be purchased with a zero-dollar balance for the in and out parker typically under 2 hours. Once the balance is running low on the card, visit the parking office at 180 Chester to have it reloaded.
The new system does not accept cash and it does not require the use of a ticket, which prevents backups from occurring when a driver is stopped at the exit and unable to locate their ticket. Monthly permit holders simply hold up their new access cards to a scanner at the entrance and exit. Previous access cards will be disabled.
In addition to these enhancements, brand new signs will be added this summer that displays the number of spots available at the structure. Those driving by the structure will easily see how many spaces are open. Eventually, all parking structures in Birmingham will have the available parking spots signs and the information will be displayed on the homepage of the City's website.
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