need help with M/M/S queuing model. attached is the question, and answer you provided. just needs to be formatted in queuing model. not sure what that is. thank you

It is a problem related with queuig theory of operation research. Trucks are coming into the que at poission pattern in 30 numbers on an average per hour. 32 trucks are cleared per hour. It follows exponential distribution pattern. You have to apply queing formulas to solve it. Therefore, 1. Average number of trucks in the system is: 2. Average time per truck in the system. It includes both waiting time in the que and serving time. 3. Utilization rates of the bin area will mean number of trucks provided in the bin through out the week to provide service. As you observed, 30 minutes a truck is taking to wait. Thus in one hour, 2 trucks can be provided to wait in that bin per hour. If service is provided for 7days in a week of 16 hours per day, then 7x16x2=224 trucks are served in a week.. Thus 2 trucks per hour can utilize bin area. 224 truck can utilize it for entire week. 4. Now you have to estimate probability of waiting of more than three trucks in the system. So at least 4 or more truck will wait in the system. Formula of probability of que size greater than or equal to k=4 is: where Therefore, 5. Total daily cost to farmers of having their trucks tied up in the system includes,cost of grain deterioration due to delay in unloading , cost of truck rental and idle driver time. It has been stated that waiting and unloadig cost is $58 per hour. As the truck is taking 30 miutes average time in the system, the cost to farmer is $58x0.5=$29 9-16 The wheat harvesting season in the U.S. Midwest is short, and most farmers deliver their truckloads of wheat to a giant central storage bin within a two- week span. Because of this, wheat-filled trucks waiting to unload and return to the fields have been known to back up for a block at the receiving bin. The central bin is owned cooperatively, and it is to every farmer's benefit to make the unloading/ storage process as efficient as possible. The cost of grain deterioration caused by unloading delays and the cost of truck rental and idle driver time are significant concerns to the cooperative members. Although farmers have difficulty quantifying crop damage, it is easy to assign a waiting and unloading cost for truck and driver of $18 per hour. The stor- age bin is open and operated 16 hours per day, seven days per week during the harvest season and is capable of unloading 35 trucks per hour, according to an exponential distribution. Full trucks arrive all day long (during the hours the bin is open), at a rate of about 30 per hour, following a Poisson pattern. To help the cooperative get a handle on the problem of lost time while trucks are waiting in line or unloading at the bin, find the (a) average number of trucks in the unloading system (b) average time per truck in the system (c) utilization rate for the bin area (d) probability that there are more than three trucks in the system at any given time (e) total daily cost to the farmers of having their trucks tied up in the unloading process (f) The cooperative, as mentioned, uses the storage bin only two weeks per year. Farmers estimate that enlarging the bin would cut unloading costs by 50% next year. It will cost $9,000 to do so during the off-season. Would it be worth the cooperative's while to enlarge the storage area