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Waiting lines, we may hate them, but they seem to be a sure sign of a civilized society. Believe it or not as an honorable and considerate person , your hard-wired to respect the queue . Don't believe me? Well let's talk about a simple waiting line situation i had faced today.
I was not even in the waiting line, i was sitting down and watching who were on the waiting line inĀ Pubali Bank(PB). All of a sudden i see someone cut the waiting line, they simply jump in front of someone already in the waiting line, how does this make you feel? I mean, who the heck does that person think they are cutting in line? They aren't special, they're just like everyone else. All people should be taken care of in the order in which they arrive. Waiting lines are important, they're important to customers, and thus they have to be important to companies. Waiting lines impact people, so which people do companies need to consider? Customers in fact , but also employees whom serve coustomers at the front of these lines. And don't forget the managers responsible of the queue system. If all those parties are not satisfied the waiting line system will not be a happy place.So,How we can find a optimum solution for waiting line?
Let's find-out!
As Waiting Lines are everywhere, every company tries to make waiting line more comfortable and customer friendly. The lines we see at banks and grocery stores and even those we can't see like when we wait on hold at a call center. How long will I wait? What are the chances there won't be line? The key to answering these questions is statistics and probability.
SupposeĀ Pubali bank BangladeshĀ has an average of six customers arrive per hour. So a customer arrives on the average every ten minutes. This bank has a single employee that can help up to ten customers per hour. On average, it takes this employee six minutes to assist each customer. Those two numbers are most that's needed to figure through the foremost basic queue problems.
Now that PB know that customers arrive six per hour and they can help 10 per hour, PB know the percentage of time their server is busy helping customers. This worker is busy 60% of the time. So one worker is busy 60% of the time. If PB hire a second worker, each of these two workers will be busy 30% of the time.Any guesses how busy the servers would be during a three server scenario? If you said 15% , nice try but perhaps rethink it. One server was busy 60% of the time. Two servers split up the work evenly so each was busy 30% of the time. So when PB hire three workers to do the work of one worker, they're splitting up 60% among three people. The servers are busy only 20% of the time.None of those workers look very busy though.
Why would PB even hire a second worker and pay them to do so little? Well, let's say Their goal is to have customers wait in line less than 90% of the time. In other words, they want 90% of their customers served immediately. What are the conditions required to have no line when they have one server? The place must be empty. If they have even one customer in bank, the next person will get in line.Trust me once I say the probability of an empty bank during this situation is 40%. So 40% of the time, PB have no line. In a two server scenario, things change. Now PB can have an empty bank or they can have one customer. Why? Because if PB have one customer, Thry have one busy server and one server that is free. The next person to arrive will not need to wait. So PB add the probability of the empty bank scenario and therefore the probability of the one customer scenario.The empty bank probability is 54%. The one customer probability is 32%. That's an 86% probability. You may wonder why the empty Bank probability went up from 40% with one server to 54%. Two servers means customers get in an out faster so there's a higher probability that the bank is empty.
How about if PB add a third server? Now They have three no line solutions.Empty bank, one customer or maybe two customers all leave PB with a minimum of one free server. The empty bank probability is 55%. The one customer probability is 33% and the two customer probability is 10%. If you add them up, you'll find PB now have a 98% probability.
So should PB hire one, two or three servers? One server would probably end in too many lines.Two servers is far better but double the wages. Three servers may be a little better than two servers and PB will got to pay three workers. Which one would PB choose? Well, it's Their business. Statistics and probability might not give them the final answer but they certainly make their choices much more clear.