In telecommunication engineering, queue’s theory is applied whenever dealing with design of telecommunication networks.
Anyhow, actually in our every day life we are all “victims” of queues. For example, when waiting to pay at the supermarket, when blocked in the traffic jam and when, as a customer, waiting the delivery of a purchased item.
Or, when dealing with Supply Chains, delivery delays and high level of stocks.
After almost ten years from University, it has been exiting for me discovered that the same principles behind the queue’s theory in Telecommunication can be applied in a totally different field where I work: logistic and supply chain.
Anyhow, which are the principles that telecommunication and supply chain management (SCM) have in common? They both could be described by using a specific statistical model “A/B/k”.
“A/B/k” is the so called Kendall’s notification A/B/k where:
- A: it represents the statistical model of new entries (e.g. a new call phone, a new client at the bank agency,…), in the queue that suit best the “real” world. For example, M stands for a Markovian (memory less) process, E an Erlang distribution process and so on
- B: it describes how the entries in the queue are processes and thus theirs statistics. It could be the same model as for arrivals or different.
- k: is number of places of the “waiting area”. If k=1 it means that new arrivals will be discharged if new entries occur. While if k=5, as an example, there are 4 places available for new arrivals till a new entry can be processed in the queue.
Apart from the statistical models characterizing arrivals and processing, when designing a simple telecommunication system there are mainly two constraint:
- the capacity of the telecommunication channel. How many calls per minute can be processed? Or how many Gbytes/s can be provided by a network connection?
- the memory available that is the number k in the Kendall’s notification.
Statistics apart, there is and hidden rule behind:
Channel capacity and Memory Available are Link each other. Low Channel Capacity might be Compensated by Increasing the Memory Available.
So, what a telecommunication network described with a Kendall’s notification have in common with SCM?
- channel capacity = velocity on handling both material and information among Supply Chain
- memory = level of inventory
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