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A digital printing studio offers personalised merchandise such as custom - printed t - shirts, mugs, and phone cases. They have recently introduced a state
A digital printing studio offers personalised merchandise such as customprinted tshirts, mugs, and phone cases. They have recently introduced a stateoftheart printing machine called the PrintMaster, capable of swiftly producing highquality custom designs on various items. The studio has launched an online platform where customers can submit their design order. Once an order is submitted, it enters a queue to be processed by the PrintMaster. A status tracker is displayed, initially showing Pending until the printing process begins. While the PrintMaster is processing the design, the status updates to Printing and once the item is ready for pickup or delivery, it changes to Ready. The design orders are uploaded to the platform according to a Poisson process, with an average of orders per day. The time taken to print each request follows an exponential distribution, with an average processing time of minutes. The studio operates continuously with no breaks and has been running long enough for steady state properties to apply. With these assumptions, the entire process can be modelled as an MM queue Suppose that on one day, no requests were submitted in the first minutes of that day. What is the probability that no requests are submitted in the next hours of that day
A digital printing studio offers personalised merchandise such as customprinted tshirts, mugs, and
phone cases. They have recently introduced a stateoftheart printing machine called the PrintMaster, capable of
swiftly producing highquality custom designs on various items.
The studio has launched an online platform where customers can submit their design order. Once an order is
submitted, it enters a queue to be processed by the PrintMaster. A status tracker is displayed, initially showing
Pending until the printing process begins. While the PrintMaster is processing the design, the status updates to
Printing and once the item is ready for pickup or delivery, it changes to Ready.
The design orders are uploaded to the platform according to a Poisson process, with an average of orders per
day. The time taken to print each request follows an exponential distribution, with an average processing time of
minutes. The studio operates continuously with no breaks and has been running long enough for steady state
properties to apply. With these assumptions, the entire process can be modelled as an MM queue
Suppose that on one day, no requests were submitted in the first minutes of that day. What is the probability
that no requests are submitted in the next hours of that day
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