batch processing proof of the number of jobs' relationship with service time and waiting time

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The classical batch processing system ignores the cost of increased waiting time for users. Consider a single batch characterized by the following parameters:

M average mounting time

T average service time per job

N number of jobs

S unit price of service time

W unit price of waiting time per user

Show that the optimal batch size that minimizes the cost of service time and waiting time per user (within a single batch) is

Equation To Be Proven

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Dane I On BEST ANSWER

Simply create a formula for the cost of service time and a formula for the cost of the waiting time per user. You'll find that these will be S/TN and WN/M respectively. Adding these gives you total cost. This is how that formula is created.