Hello,
For an assignment I'm looking at a workplace situation where products are handled by several servers. These products have to be entered in several administrative computer systems and afterwards they can be inspected physically. In the 'old' situation, the servers do both of these actions when the product has actually arrived at their station. In the 'new' situation however, pre-alerts will be sent indicating that the products will arrive at the workplace after a certain amount of time. This makes it possible to enter the products in the administrative systems before they have actually arrived. As a result, the products only have to be inspected when they finally arrive. I want to determine how many servers are needed at the workplace to make sure that (almost) all products are in the administrative systems before they arrive. Therefore, I was wondering if Enterprise Dynamics offers any possibilities to tackle this problem? I also have a few related questions:
- Can I implement a situation where certain products always have to be completed before other products (i.e. a product representing a pre-alert always has to be finished by the server before this server or another server can start with a product representing the actual inspection)? This means that these two products somehow have to be related (one being the pre-alert and one being the actual arriving product). Can this be done?
- Can I somehow link two arrival processes? For example: in the morning 7 pre-alerts arrive and then in the evening 7 corresponding products arrive. And can this be done while using a poisson arrival process for the actual products?
Pre-alerts
Re: Pre-alerts
Hi,
I made a small example for your which covers the questions from your post, it gives you my suggestions to model this problem. Please have a look at the attached model:
1. The arrivallist generates an amount of products 08.00 AM representing the pre-alerts.
2. Directly afterwards you'll find a splitter that sends the pre-alerts into 1 queue and a copy into another queue, these copies represent the actual arrivals for inspection.
3. The queue directly in front of the server has a modified Queue Discipline: the products having a label prealert will be put in front.
4. For the time until inspection I implemented that the inspection tasks will arrive randomly between 10.00AM and 05.00PM (2-9 hours after prealert). This will result in a poisson (or negative exponentional) time distribution between the products arriving in the queue waitinginspection.
Another solution could be to replace the multiserver by a queue with a big capacity followed by a server. Give the server a process time of Poisson(10) where 10 is the mean value, would also result in arrivals at the queue WaitingInspections that are independent of each other.
Hope this gives you an idea how to continue, good luck!
Regards, Marlies
I made a small example for your which covers the questions from your post, it gives you my suggestions to model this problem. Please have a look at the attached model:
1. The arrivallist generates an amount of products 08.00 AM representing the pre-alerts.
2. Directly afterwards you'll find a splitter that sends the pre-alerts into 1 queue and a copy into another queue, these copies represent the actual arrivals for inspection.
3. The queue directly in front of the server has a modified Queue Discipline: the products having a label prealert will be put in front.
4. For the time until inspection I implemented that the inspection tasks will arrive randomly between 10.00AM and 05.00PM (2-9 hours after prealert). This will result in a poisson (or negative exponentional) time distribution between the products arriving in the queue waitinginspection.
Another solution could be to replace the multiserver by a queue with a big capacity followed by a server. Give the server a process time of Poisson(10) where 10 is the mean value, would also result in arrivals at the queue WaitingInspections that are independent of each other.
Hope this gives you an idea how to continue, good luck!
Regards, Marlies
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enterprisedynamics
- Posts: 14
- Joined: Tuesday 29 March, 2011 - 09:12
Re: Pre-alerts
Hi Marlies,
Thanks so much! I know now that the pre-alerts arrive every morning and the corresponding products the next day according to a poisson process. Am I right in thinking that I can model this by having the actual products sent to a multiserver with enough capacity where they are served for e.g. 12 hours (exactly 12, no probability distribution) and afterwards have them sent to a queue and afterwards a single server with e.g. Poisson(10) process time like in your suggestion? By the way: should this be Poisson(mu) or NegExp(mu)? Because I believe that when the interarrival times are negative exponential, then the corresponding arrival process is Poisson distributed? The interarrival times being the processing times of this single server like you suggested.
Thanks so much! I know now that the pre-alerts arrive every morning and the corresponding products the next day according to a poisson process. Am I right in thinking that I can model this by having the actual products sent to a multiserver with enough capacity where they are served for e.g. 12 hours (exactly 12, no probability distribution) and afterwards have them sent to a queue and afterwards a single server with e.g. Poisson(10) process time like in your suggestion? By the way: should this be Poisson(mu) or NegExp(mu)? Because I believe that when the interarrival times are negative exponential, then the corresponding arrival process is Poisson distributed? The interarrival times being the processing times of this single server like you suggested.
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enterprisedynamics
- Posts: 14
- Joined: Tuesday 29 March, 2011 - 09:12
Re: Pre-alerts
I meant 24 hours instead of 12. This multiserver should lead to the system being 'in the next day'.
Re: Pre-alerts
Hi,
Yes, you could model it like that. Then the processtime of the server should be negexp(mean). It's indeed like you wrote: when the interarrivaltimes are negative exponentionally distributed, the arrival process itself (the number of arrivels per time unit) is poisson distributed.
Regards, Marlies
Yes, you could model it like that. Then the processtime of the server should be negexp(mean). It's indeed like you wrote: when the interarrivaltimes are negative exponentionally distributed, the arrival process itself (the number of arrivels per time unit) is poisson distributed.
Regards, Marlies