QUEUEING THEORY AND ITS APPLICATION TO ROAD TRAFFIC CONGESTION BY CHIEDU NELSON CALED PSC060774 A PROJECT WORK PRESENTED TO THE DEPARTMENT OF MATHEMATICS‚ FACULTY OF PHYSICAL SCIENCE‚ UNIVERSITY OF BENIN IN PARTIAL FULFILMENT OF THE REQUIREMENT OF THE AWARD OF BACHELOR OF SCIENCE (B.SC) (COMBINED HONOURS) DEGREE IN STATISTICS AND COPMPUTER NOVEMBER 2012. CERTIFICATION This is to certify that this project was carried out by CHIEDU NELSON CALEB of the Department of Mathematics
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Lab 2 2.2.1 The mean arrival rate of the number of users in a particular cell making a call in the busy hour and the time interval of those calls is calculated. Every user makes a call in an interval by using the uniform random number. If this number exceeds 1-mean arrival rate or is equal to the mean arrival rate‚ then a call is generated which is referred as poisson threshold. 2.2.2 In this case the green line indicated the poisson threshold. When the customer uniform random number exceeds
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QUEUING THEORY Definition A queue can be defined as items awaiting service. Queues may consist of people‚ cars‚ components awaiting machining‚ telephone calls‚ aeroplanes‚ indeed any discrete items. Queues form when the rate of arrival of items requiring service is greater than the rate of service. Queuing theory can be defined as the construction of mathematical models of various types of queuing systems so that predictions may be made about how the system works with the demands
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increased or decreased slightly. Will such changes affect the optimal solution ? The Input or Arrival Process •The input process is usually called the arrival process. •Arrivals are called customers. •We assume that no more than one arrival can occur at a given instant. •If more than one arrival can occur at a given instant‚ we say that bulk arrivals are allowed. •Models in which arrivals are drawn from a small population are called finite source models. •If a customer arrives but fails
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373 Topic: Characteristics of a Queuing System Difficulty: Moderate 4) The average time each customer spends in the queue is referred to as: A) W B) Wq C) L D) Lq E) ρ Answer: B Page Ref: 377 Topic: Single-Server Queuing System With Poisson Arrivals and Exponential Service Times (M/M/1 Model) Difficulty: Moderate 5) In a drive-in fast food restaurant‚ customers form a single lane‚ place their order and pay their bill at one window‚ and then pick up their food at a second window. This queuing
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Analyzing Waiting Lines Most people find waiting lines irritating – waiting is idle and nonproductive time. From a service system perspective‚ however‚ a line represents a demand for service. Think of a restaurant on a Friday night. As a customer it is an irritation to have to wait 40 plus minutes for a table‚ but from the restaurant’s perspective‚ if there is not a line‚ then that means there are empty tables. Idle services are not good. So management must balance waiting time with the
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industry reached an all-time record of 760 million international tourist arrivals in 2004. The figure represented an increase of 10 percent in comparison with the previous year‚ the best results in two decades‚ according to a report released by World Tourism Organisation. The Organisation said year 2005 was even better‚ with Asia benefiting not seen before. 2.1 Malaysia Tourist Arrivals and Receipts to Malaysia: Year Arrivals Tourism Receipts (RM) 2000 10.22 million 17‚335.4 million 2001 12
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under the Mongol rule due to various improvements instituted by the Mongols that helped encourage trade. However‚ overspending eventually majorly contributed to its demise. Dissimilarly‚ Russia’s economy was falling apart at the seams‚ and the Mongol arrival helped relatively stabilize it. In both Russia and China‚ however‚ the Mongols dominated the government. The formation and conquests of the Mongol Empire was very influential both politically and economically on China and Russia in various ways.
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underloaded‚ waiting lines tend to form if arrival and service patterns are highly variable because the variability creates temporary imbalances of supply and demand. 3. All of the waiting line models presented in the chapter (except the constant service time model) assume‚ or require‚ that the arrival rate can be described by a Poisson distribution and that the service time can be described by a negative exponential distribution. Equivalently‚ we can say that the arrival and service rates must be Poisson
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Foreign visitor arrivals: 6.8 million (+13%); Domestic visitors: 32.5 million (+8%); Tourism receipt: USD 7.7 billion (+23 %). Table 1. The major indicators of Viet Nam tourism in 2012 Number of Foreign Visitor Arrivals Number of Domestic Visitors Tourism Receipt (US$ Millions) in 2012 Hotels Number of Star and Non-Star Hotels Number of Star and Non-Star Rooms Number of 3-5 Star Hotels Number of Rooms in 3-5 Star Hotels Average Occupancy Rate in Non-Star and Star Hotels (%) Foreign Arrivals by Mode of
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