derive an expression that prescribes the machine’s capacity (µ) as a function of T and λ . (Capacity is defined as the number of orders the machine can handle per day.) What happens to the required capacity when T is decreased to 0?
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A make-to-order system is well described as a basic Erlang system with a single machine. The manager of the system wants to ensure that the expected turnaround time of any order (from its placement until its shipment to the customer), in days, is T. If orders arrive at a rate λ per day, derive an expression that prescribes the machine’s capacity (µ) as a function of T and λ . (Capacity is defined as the number of orders the machine can handle per day.) What happens to the required capacity when T is decreased to 0?
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- A server operates with 70% utilization. The coefficient of variation for the service process is 0.6 and the coefficient of variation of the arrival process is 1. The average processing time is 3 minutes. What is the average time a customer spends in the system according to the single-server queue model? A. 9 minutes B. 6 minutes C. 3 minutes D. 7.5 minutes Consider an Erlang loss system. The average processing time is 6 minutes. The average interarrival time is 3 minutes. The number of servers is 9. What is the capacity of the system? A. 0.8 customers per minute B. 1.5 customers per minute C. 1.1 customers per minute D. 2.4 customers per minuteA copier store has four pieces of automatic equipment, but sometimes they are down because they need supplies, maintenance or repair. Each unit requires about two services every hour or, to be exact, each piece of equipment runs an average of 30 minutes before needing service. Service times vary greatly, from a simple service (such as pressing the reset switch or replenishing the paper) to disassembling the equipment in question. However, the average service time is five minutes. The time the equipment is down generates a loss of $60 per hour. The single employee who services the equipment earns $18 per hour. Using finite population analysis, answer the following questions: a. What is the average number of units idling? b. What is the average number of units still operating? c. What is the average number of units being serviced? d. The company is considering adding another manager at the same wage of $18 per hour. should it do so?Suppose that documents are transmitted by a facsimile machine. Assume that the documents arrive at random, 75% of which is of the fixed form with constant transmission (service) time 40 seconds, whereas the rest are exponentially distributed with the mean 2 minutes. 1. How many documents per hour can be transmitted with mean waiting time no greater than 30 seconds? 2. If the number of documents per hour is the same as (1), and if all documents are of the fixed form, how much is the mean waiting time? Please answer both 1 and 2 with a complete step and formula used.
- Consider an Erlang loss system. The average processing time is 3 minutes. The average interarrival time is 2 minutes. The number of servers is 4. What is the probability that all servers are busy?A graphics reproduction i rm has four units of equipment that are automatic but occasionallybecome inoperative because of the need for supplies, maintenance, or repair. Eachunit requires service roughly twice each hour, or, more precisely, each unit of equipmentruns an average of 30 minutes before needing service. Service times vary widely, rangingfrom a simple service (such as pressing a restart switch or repositioning paper) to moreinvolved equipment disassembly. The average service time, however, is i ve minutes.Equipment downtime results in a loss of $20 per hour. The one equipment attendant ispaid $6 per hour.Using i nite queuing analysis, answer the following questions:a. What is the average number of units in line?b. What is the average number of units still in operation?c. What is the average number of units being serviced?d. The i rm is considering adding another attendant at the same $6 rate. Should the i rmdo it?In a queuing model which follows the single server operation has ? = 2 and ? = 8. The evrage number in the system Ls is ____ and the utilization of the system is ____ a. 0.33 ; 25% b. 3 ; 100% c. 6 ; 25% d. 4 ; 33%