Global Journal of Researches in Engineering, J: General Engineering, Volume 22 Issue 1

referred to as traffic intensity which lies between zero (0) and one (1) (Okoko, 2000). It must be less than 1, otherwise there will be an infinite queue and the system needs to operate for a long time to return to a steady state – where arrival rate can be easily managed by the system’s service facilities at any time. Generally, customers may display different types of behaviour when they see a long queue on arrival (Ojo and Adebisi, 2018). Where customers decide to leave the line or queue without being served is known as Reneging or Abandonment. Where customers do not join the line but try to look for any available opportunity to enter the queue illegitimately is referred to as Baulking or Shunting. Others may move forward and backward in-between queues, looking for a fast-moving queue, thereby exhibiting a behaviour known as Jockeying. In queue theory, a model is constructed so that queue lengths and waiting times can be predicted (Anokye, et al. 2013). This also helps in predicting the number of servers that will be needed in a system for cost minimization and profit optimization. A reduction in the average service time, E(t) through the addition of another service point will lead to a further reduction in the average queue length and waiting time as well as other queue performance measures especially in a multi-channel situations (Odior, 2013). Queue Modeling as a mathematical one involves formulation of mathematical equations and it is useful in making some predictions about any system of study. The model is an offshoot of either probabilistic or stochastic modeling. Queue studies involve a number of systems. These consist of four sub-systems, comprising arrival pattern, a queue discipline, service facility and the outlet. The arrival pattern concerns ways through which trucks or items come into the system in a discrete manner. The queue discipline describes the arrival time of items versus when the service is performed and this follows some set of rules i.e. first come, first served or last come, first served. The service deals with the length of time a customer is served, i.e. number of servers and the service pattern. The length of time to serve a customer is known as the service rate. The queue in the system can be single or multiple and service points can be single and multiple too. However, the service rate normally has a negative exponential distribution. The outlet is the exit or departure from the system and this can influence the arrival and service rates in one way or the other (Wright and Ashford 1989; Lucey 1992). At Solous III dumpsite in Igando, Lagos State, it is a recurrent decimal to find waste trucks forming long queues on both sides of LASU-Iba Expressway waiting for long period of time before being served. Frequent maneuverings of these trucks creates incessant traffic congestion which result in huge man-hour loss to commuters and motorists (Olorunfemi, 2003). Delays experienced by these trucks before service is rendered, affect their level of turn-around and this level of performance of the dumpsite have implications for the city’s waste management (Odewunmi, 2004; Taylor, 1994). This development informed the interest to study the likely causal factors of such long queues of trucks at the Solous III dumpsite at Igando, Lagos State towards evolving some useful way to manage trucks at the dumpsite. a) Objectives of the study i. Evaluate the queue system parameters such as the arrival rate, the service rate and the traffic intensity of trucks at Solous III dumpsite, Igando, Lagos State. ii. Determine the queue systems performance measures such as the number of trucks in the system and in the queue, the waiting time of trucks in the system and in the queue as well as probabilities of events (trucks) at the dumpsites, iii. Suggest some ways to improving dumpsites performance measures at Solous III dumpsite, Igando, Lagos State. b) Hypothesis Testing The study will also test the following hypothesis, as a way of validating the results of this research work. H o : Trucks Arrival rate does not follow a Poisson distribution at the dumpsite. H 1 : Trucks Arrival rate follows a Poisson distribution at the dumpsite. II. M ethodology: u sing M/M/I Q ueue M odel Data collection process for this study was based on Arrival rate and Service rate of Trucks at Solous III dumpsite situated along LASU-Iba Expressway at Igando, Lagos State. Solous III is the only functional dumpsite within Igando Area at the moment where trucks arrive in a Poisson process, discharge waste and exit the system after service has been completed (Magnus, 2015). This is synonymous to what is known as birth and death process in queue system. Birth refers to the arrival of trucks to join the existing queue at the dumpsite and death means departure or exit from the system having received service (Gross and Harris, 1985). It is assumed that the time interval between successive arrivals and service time is independent and identically distributed especially in a simple queue formation (Anokye, et al 2013). A queue is said to be simple queue, if it is a single queue, single server and the pattern of arrival follows a random type and Poisson probability distribution. On the other hand, the service time is also random, having a negative exponential distribution (Wright and Ashford 1989; Lucey 1992). The queue system adopted at the dumpsite is a simple queue model (M/M/I) and a queue discipline of First-Come-First-Served (FCFS) and data were collected Improving Trucks Management at Dumpsites through the Application of Queue Theory- The Case of Solous III Dumpsite, Igando, Lagos State lobal Journal of Researches in Engineering ( ) Volume XxXII Issue I Version I J G 32 Year 2022 © 2022 Global Journals