# Using queuing theory to solve the problem of momentum to issuing the driving licenses in Dohuk city

## Authors

• Nabeel G. Nacy Department of Statistics, University of Salahaddin, Kurdistan Region, Iraq
• Samaher T. Ibrahim Department of Statistics, University of Duhok, Kurdistan Region, Iraq

## Abstract

Queuing theory is a mathematical study of so-called queues or waiting lines. This phenomenon is common in daily life as in gas stations, airports, repair workshops and other common everyday examples. Waiting occurs when service demand is higher than service system power. Due to the difficulty in predicting the number of customers arriving and the time taken by the customer at the service station, the process of obtaining performance metrics is necessary before the queuing systems are implemented. When the service system power is too high, the system is charged at a high cost. Conversely, when the system power is low (insufficient for the customer service), the waiting time in the queue increases, As well as loss of order to its customers. Therefore, attention has been drawn to the so-called theory of waiting lines to solve such problems to reach a balance in the work of the system.

This research aims to overcome the difficulties experienced by citizens in obtaining market holidays on time and reduce waste in time and the cost of waiting.

The results were as shown in tables (l) to (6) of the city center and according to the distribution of access and service of the model used (G / G / C). We note in the Poisson distribution with exponential that the average number of customers in the system Ls = 5.527), which is approximately (5 customers), which is waiting in the system. We note in the previous distribution itself that the average number of customers in the waiting queue (customer 2.1924 = L q) is approximately 2 (customer) which is waiting in queue. The Poisson distribution with the exponential is that the average time spent by the customer in the system (minute W s = 16.5772). Note in the Poisson distribution with the exponential that the average time spent by the customer in the waiting queue is (minute W = 6.5772) We note in the Poisson distribution with exponential that The average number of customers in the system (customer Ls = 4.3258) is about (4 customers) which is waiting in the system. We see in the previous distribution itself that the average number of customers in the queue (customer 2.0 = L q) ) There is no waiting in the queue. The Poisson distribution with exponential is the average time spent by the customer in the system (min W s = 11.3333). We note in the Poisson distribution with exponential that the average time spent by the customer in the waiting queue is (min W q = 4.6666)

## References

1. Ammar, Shehab Ahmed (2007), applications for the theory of waiting lines in the teaching hospital of the Faculty of Dentistry Baghdad University / Master of Operations Research / Faculty of Management and Economics / University of Baghdad.
2. Dakheel, F. I (1990),"A decision Support system for Single stage Markovian Queuing system " , Ph. D.thesis, University of Brad Ford; UK.
3. Dridi, Dreams. The role of using queuing models in improving the quality of health services. (2013/2014). Mohammed Khader University. Democratic People 's Republic of Algeria.
4. Evans, James R. (1992)"Applied production and operations Management ", 4th edition,west publishing company; USA.
5. Government, Rajab Abdullah and Asbakia / Mansour Ramadan (2004) "Applications of queues at the Marine Services Center". Http: // www. Culturecarner / nreory.uk
6. Hiller, Frederick S.& Lieberman Gerald J., (2001), "Introduction to operations Research", 7th edition, McGraw- Hill Inc. USA.
7. Samuel A.E& Venkatachalathy M.,(2014) , " improving izpm for Unbalanced fuzzy transportation problems " Intermtional journal of pure and applied Mathematics ,vol 94, no 3,p.p :419.
8. Taha, Hamdy A. (1997) "Operations Research: an Introduction", 6th edition, Prentice – Hall. Inc. New Jersey, USA.
9. Taha H.A,(2007) ,"Operations .Resarch An Introdution" , 8th , prantice Hall of India private Limited , New delhi.
10. Zalka, Zakaria Mohammed Deeb (2006) "Models of the waiting queues and their uses in the transport traffic at Damascus International Airport / Master Thesis in the Department of Statistics / Faculty of Management and Economics / University of Baghdad -

2019-10-21

## How to Cite

Nacy, N. G., & Ibrahim, S. T. (2019). Using queuing theory to solve the problem of momentum to issuing the driving licenses in Dohuk city. Academic Journal of Nawroz University, 8(4), 136–143. https://doi.org/10.25007/ajnu.v8n4a453

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