Abstract. 1 Introduction

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1 Transactions on the Built Environment vol, 995 WIT Press, ISSN Application of queuing theory on the design of fishing harbors U.GOkkup Department of Civil Engineering, Faculty ofengineering, CelalBayar University, 454 Manisa, Turkey Abstract In order to determine an optimum number of berths of a fishing harbor, the queuing theory is applied in the light of the national fishing vessel, harbor and activities. Waiting time of fishing outside the harbor and in queue is calculated in accordance with the considered queuing model. Here, the theoretical distributions representing the actual vessel arrival and service time distributions are determined. For the economic considerations, cost estimate studies including cost of harbor and waiting are carried out. Both proposed mathematical and economical model are applied on Guzelbah^e fishing harbor. Introduction It is known that a harbor is the facility composed of the naturally or artifically sheltered water area, water-landside facilities to provide some utilities and services for ships and cargo handling equipment. Until now, there were no any cargo handling equipment located at the quay and landside facilities. But in recent years, it is seen that the number of these facilities has been increasing. By becoming small capacities of these facilities and lacking the various cargo handling equipment, and differing its administration and management structure, it can only seperate from port and port system. In general, harbors have national characteristics. Their contributions to the national economy are not large scale with respect to the ports. And their equipments can only handle the special type cargo in convenient with their functions. At the stage of planning harbors, capacities and dimensions of water and landside facilites should be optimum from economical and technical point of view. In order to determine the capacities of the facilities, The number and characteristics of ships to use the harbor, their arrival time and service time frequency, seasonal and daily time series of ships during arrival and service,

2 Transactions on the Built Environment vol, 995 WIT Press, ISSN Marine Technology and Transportation total number of ships to come there during storm durations should be known before planning a fishing harbor. In design, the dimensions of berthing and landing places and maneuvering line for ship traffic, inner-sheltered water area of a harbor, should be convenient to respond to the whole demands of ships. For this case, daily activities of the ships and functions of harbor should be considered. In this study, the aim is to apply the mathematical optimization technique in planning of a fishing harbor in the light of the above-mentioned informations and determine the optimum sizes of the facilities. Therefore, the statistical data types required for a fishing harbors, their functions and special operation principles are investigated and queuing theory in evaluating ship statistical data is applied. 2 Functions of a Fishing Harbor A fishing harbor will provide the serice forfishingboats, crews and fishing products. Therefore it should include the required facilities in waterside and landside. The functions of a fishing harbor are composed of safe entrance position, depth and width; the type of berths and their layout with anchorage areas and turning basin with easy access to berths; breakwaters to provide the sheltered water area; utility services and building for display auction and sales in landside; easy connection to the road and railroad for rapid transportation; and navigational aids and lights. (2) 3 Water and Landside Facilities of a Fishing Harbor The facilities necessary for developing the harbor consist of the necessary facilities for, the products and the staff located at the water and landside. Waterside facilities are protective structures (i.e. breakwaters, bulkheads, groins, revetments), navigational aids, anchorage basin, open and covered moorage, and quays. Landside facilities are also composed of preparation hall, cold storing and packing hall, freezers, water and ice-supply facility, warehouses, administration and management building, fishermen's co-operative, auction and marketing hall, fish processing facilities and repair-maintenance building. (6) The capacities and sizes of these facilities directly depends on the number and size of ships, the arrival and service time frequencies,and the tonnages of fishing products. For this reason, statistical informations on ship traffics are evaluated by using the Queuing theory to find the optimum berth number to affect the dimensions and capacities of water-land side facilities.

3 Transactions on the Built Environment vol, 995 WIT Press, ISSN Marine Technology and Transportation 73 4 Fishing Harbor Planning In general, harbor planning can be carried out two phases: () Economical planning ;estimating the optimum harbor size and number of the berths, (2) Engineering planning; that is the engineering investigations including hydrographical and topographical survey, meteo-oceanographical survey, coastal hydrodynamic studies and soil testing, site selection, and the general harbor layout. In engineering planning, site selection is composed of some studies such as water depth and soil condition, sheltering needed against incoming waves, currents and littoral drift, existing town or village and commercial facilities, rail and road connections, hinterland development possibilities and availability of building materials near the site. At the zone selected for harbor, harbor layout can be carried out by considering safe natural or artificial sheltering, initial cost required for obtaining adequate deep quays, easy entrance to the harbor and easy turning basin for ship traffics. Entrance should not be open to the direction of prevailing waves, currents and littoral drift. The depth of entrance should be suitable to allow the largest draft ship coming to the harbor. The entrance width depends upon the beam, speed and maneuverability of maximum size of the fishing vessel, whether the vessel is to pass another vessel, the design depth and the height, direction and frequency of winds, waves and currents. Turning basin is a circular form or half-circle form where the vessel may turn around a corner of the quay. It can be determined in proportion to the lenght of the largest vessel. The depth of basin for fishing vessel should be between m. The size of berthing places for handling can be calculated in accordance with the beam and lenght of vessel. (9,) The layout and dimensions of breakwater depend on the direction of the maximum waves, the configuration of the shoreline and the minimum size of the harbor required and should prevent the extreme oscillations in front of the quays. From the economic planning point of view, thefishingharbor is the complex of installations on land, organized to service the fishing fleet and its cargo, and is the main link in the production chain of all components of the fishing industry, which should efficiently performe their tasks, with the aim of achieving the planned targets with the minimum cost. This definition formulates the problem of port planning in such a way that the planned results should be optimum, that is, the results of all components should minimize total costs. (7)

4 Transactions on the Built Environment vol, 995 WIT Press, ISSN Marine Technology and Transportation Decision problems concerned with the optimum harbor size which yields the most economical transfer of cargo between the ship and harbor is a difficult task since it depends upon many operational parameters of fluctuating values such as amount of cargo, randomness in ship arrivals, queue discipline, the distribution of service time (time used for loading and unloading), seasonal and monthly variation aof ship arrival rates, bed weather conditions and others. The basis for economic considerations which should yield the optimum harbor size (optimum number of berths) is a sufficient knowledge of the amount of cargo to be handled in the harbor. Traffic forecasts are made to estimate the trends and amount of cargo to be loaded and unloaded in the harbor in future. The traffic forecast is preliminary based on traffic statistics from the past years, hinterland development and general economic development in the country. Since determination of the amount of cargo expected is of great importance to make reasonable economic considerations regarding the optimum size of the harbor, traffic forecast has to be carried out preferable covering the entire estimated economic life time of the harbor. () For decision making an optimum harbor planning the mathematical technique, Queuing Theory is valuable method applied to estimate the waiting time of ships in a harbor depending on the statistical distributions of the ship arrivals and berth service time. 5 Definition of Queuing Theory Queuing theory involves the mathematical study of queues, or waiting lines. The waiting phenomenon is the direct result of randomness in operation of service facility, and customer's arrivals. The principal elements in a queuing situation are the customer (ship) and the server (handling equipment). In queuing models, customer arrivals and service times are expressed in terms of probability distributions normally referred to as arrivals and service time distributions. These distributions may present situations where customers arrive and are served individually. The pattern of arrivals and departures are the main factors in the analysis of queues. The first factor is the manner of choosing customers from the waiting line to start service. This referred to as the service discipline. In practical situations, this may arise as the FCFS (First Come First Served), LCFS (Last Come First Served) and SIRO (Service in Random Order). The second factor deals with the design of the facility and execution of service. The facility may include more than one server. AH servers offer the same service and the facility is said to have parallel servers. If any customer has to take the different service from all

5 Transactions on the Built Environment vol, 995 WIT Press, ISSN Marine Technology and Transportation 75 servers, in this case, the series processing will arise. The third factor concerns admissible queue size. In certain situations, only a limited number of customers may be allowed, possibly because of space limitation. The fourth factor deals with the calling source which may be capable of generating a finite number of customers or (theoretically) infinitely many customers. A finite source exists when an arrival affects the rate of arrival of new customers. Generally, some informations should be defined to apply queuing model in practical situations. These informations and patern to be considered in this study are; () Customer population (infinite), (2) Number of channels (multiple-parallel), (3) Queue discipline (FCFS), (4) Arrival distribution (Poisson), and (5) Service-time distribution (Negative Exponential). (5,6) Before setting up any model, it is necessary to check the theoretical arrival and service time distributions with observed ones. Such a compatibility analysis can be carried out by a well-known Goodness of Fit test, namely Chi-Square test. Ship Arrival-Time Distribution: the arrival of ship into a port are generally randomly distributed. This generallyfitsto Poisson Distribution Pn(t); P»(t)= n=,l,2,.. () n! Here, X is the arrival rate, t is the interarrival time Service-Time Distribution: for this model, the more convenience of the negative exponential distribution is conveniently found with respect to the others. where Py is the negative exponential distribution, and b is the service rate. (2) 6 Queuing Model Selection For this study, the fishing harbor is assumed to be multiple service station system, unlimited queue where the queue discipline is considered as FCFS. Further, the theoretical ship arrival and service time distributions are respectively assumed to be Poisson and Negative Exponential Distribution. According to the Kendall notation, the asumed model can be expressed as (M/M/c). For this model, the following expessions which composed of

6 Transactions on the Built Environment vol, 995 WIT Press, ISSN Marine Technology and Transportation probability of zero ship in harbor (Po), expected number of ships in queue (Lq), expected number of ships in harbor (Ls), expected waiting time in queue (Wq), expected waiting time in harbor (Ws), are derived; (,2) o-l P" P' Po={Z }-' (3) n= n! c! (-p/c) (c-)! (c-p/c)' Ls- Lq+p (5) Lq Wq= ---- (6) Ws= Wq+ (7) H where p is the traffic intensity (X/ji), \JL is service rate. 7 Pricing Structure of a Fishing Harbor in TURKEY Once the projection of harbor traffic is made, the harbor size that is the number of berths required will be determined by operational analysis to optimize the harbor investment. The analysis will indicate the optimum number of berths taking into account all cost elements and maintenance of harbor structures, cargo handling equipment and the operational cost. Cost of ships is due to waiting time, time spent by the ship in harbor in awaiting of berth to become vacant. The randomly distributed ship arrivals and the service time has all influence on the waiting time. (6,2) Cost of Harbor: Cost of structures has to be calculated on annual basis, depending on the type and size of structure and construction depth. This cost consists of cost of berth and breakwater in addition to their maintenance costs. The following formula gives the cost of structures (C ); (8)

7 Transactions on the Built Environment vol, 995 WIT Press, ISSN Marine Technology and Transportation 77 where LB is the lenght of a berthing place, LW is the lenght of breakwater, M is the number of the berths, R is the capital recovery factor, CBU is the unit cost of berth, and CBWU is the unit cost of breakwater. Cost of maintenance can be taken as 2.5 percent of the structural cost. However, the cost of harbor (Cs) is written as follows; Cy=.25 Cs (9) Here, the cost of landside facilities depending on the number and width of berths is not taken into account. Cost of Ship. This arises from the ship waiting in the queue because of insufficient number of berths. Therefore, the fishery harbor users loose money due to waiting time of the ship. In this study, the fishermen's co-operative associaction is assumed to be established to manage the fishing harbor activities. Then the computation of the ship cost is based on the assumption that all fishermen are the member of the fishermen's co-operative association and all the fishing boats are owned by the co-operative association hence all fishermen work for the cooperative association. In return, fishermen welfare is secured by this association. The basis for the wages of the fishermen which is payed by the co-operative association is determined according to so-called "share system". In this sysytem, hourly wages of a fishermen is computed as aportion of the total catch of the vessel. Since the fishermen is worked on hourly base, fishermen's co-operative association has to pay extra money for the fishermen, if the ship has to wait in the queue. In this case, extra payment can be taken as cost of ship. Annual cost of ships CSH can be taken computed for the average daily waiting time of ships; (6,7,2) CsH= Tw N CR Sh Ty n R/6 () where Tw is the average daily waiting time for a ship (average ship size), N is the total number of ships using the harbor, CR is the number of fishermen in the average ship size, SH is the hourly salary per crew, Ty is the number of working days in a year and n is the economic life of the investment. 8 Case Study: GCZELBAH E FISHING HARBOR In this study, traffic data of Guzelbahge Harbor is analyzed, where queuing theory technique was used to assist in determining the optimum number of the berths. This harbor is located on the west of the Izmir city and approximately km away from Izmir. It has fishery cooperative which has

8 Transactions on the Built Environment vol, 995 WIT Press, ISSN Marine Technology and Transportation 5 registered and almost 3 to 5 unregistered fishing vessel using the harbor. Handling is carried out by ship gear. Data on Ship Arrivals: The arrive randomly at the harbor between 4 and 2 o'clock. Table..gives the ship arrival frequency with 3-minutes interarrival time. n t Table.. Data on ship arrivals Data on Time Spent at Berth: this is named as the service time. Table 2 shows the vessel service time distribution. Berth service times (min) DisL of by their lenght (m) Table.2. Data on Time Spent at Berth lenghts % uctuol no. of CumuL no. of Distrib. % Theor. % Distrib. no. of Theory no. of X^ N=2 X*=9.22 Analysis of Data: according to the queuing model selected, the ship arrival and service time distributions can be accepted adequately fit respectively to Poisson and Negative Exponential Distribution with a confidence level of more than 99 percent. After optimization process, the costs are calculated. Minimum total cost is obtained as 3 USD TL with 8 berths 9 Conclusion Fishing activities have national characteristic features. This situation causes changing of cost estimate studies and queuing model. In this time, various type queuing model should be set up. In the determination of theoretical arrival and service time distributions, goodness of fit test must be applied. When these distributions do not satisfy and fit the actual ones, Monte-Carlo Simulation method should be applied in determining the waiting time of in queue.

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