Fuzzy Data Flow Control Of Communication Network With Infinite Terminal

The problem considered is that of optimally controlling a queueing system which consists of a common buffer or queue served by three servers. The system objective is to assign customers dynamically to idle servers based on the state of system so as to minimize the mean sojourn time of customers. Simulation shows that this approach is efficient and promising, especially in cases where analytical solutions do not exist. 1.Problem Statement and SolutionFig.1 communication network model with infinite terminalThe queueing system shown in Fig.l is considered. Only one customer can arrive per slot. Arrivals to the buffer form a random rate p .The batter is served by three servers with different mean server times. The service time of a customer at server i is u(i)(i= 1,2.3). Without toss of generality we assume ul>u2>u3.We wish to minimize the sojourn time of customers in queueing systemThe state of the system can be described by (x,yi,y2,y3)where x=0,l,2"-is the number of customers in the buffer and y(i)=l ,0 indicts whether server i(i=l ,2,3)is busy or idle. If y(i)=1 then server i is busy. If y(i)=0 then server i is idle. The state of thesystem can be divided into several cases as follow:1) x=0. if there are no customers in the queue, regardless of whether the servers are busy or idle, then no customers are allocated to any server in the system.2) x>0. yl=0,if the fastest server is idle and there are customers in queue, then a customer is allocated to this server.3) x>0,yl=l,y2=0,if the fastest server is busy and server 2 is idle while there are customers in queue. only we need consider the customer is allocated to server 1 or server 2.4)x>0.yl=l,y2=l.y3=0, only the slowest server is idle and there are customers in queue, we are interested in his state.5) x>0,yl=l,y2=l,y3=l,system is busy. Though there are customers in queue, no customers are allocated to any server.From above consideration, we are interested in state 3 and state 4.At each decision we observe the queue size. The longer the queue the easier ft is to make the decision to allocate a customer to idle server. However we need additional information to determine the quantitative relationships between the queue size and final decision. To overcome this difficulty, we make use of the customer arrival rate P .In state 3: xX).y 1=1 .y2=0 (y3=0 or \3=1). server 1 is busy and server 2 is idle while there are customers in queue. The customer has two choices: ã‚œeing allocated to server 2. (gXvafting until server 1 is idle then being allocated to server 1. Obviously, the larger P ZO, PS, PMPBo The larger x is, the longer queue is, and more easily a customer is allocated to server 2.How can we decide as to minimize the mean sojourn time of customers in the queueing system? We can use fuzzy control to solve the problem.In addition to the above crisp rules, we set up the fuzzy rule as follows. Thenumber of queueing customers x=0.1,2,3......and mean arrival rate of customers Pserve as fuzzy inputs and the decision of d=l .0 to allocate a customer to idle server 2 as output The universes of discourse for the fuzzy input x and P are[0 , 9]and[0,6] .respective!}. The universe of discourse for the fuzzy output d is[0, 1 ] r Weselect five values for variable x: ZO. PS, PM,PB, PVB. We select four values for variable P:ZO, PS, PM.PBo PVB indicates "positive very big", which is larger than PB and YES and NO for fuzzy output d correspond to one and zero, respectively. If YES is obtained, a waiting customer is allocated to the idle server 2,otherwise there is no allocatioaFuzzy rules can be described as follows:if x is ZO and P is ZO then d is NOifxisZOand P is PB then d is NOif x is PVB and P is PM then d is YESifxisPVBand P is PB then d is YESWe determine the quantitative relationships among the fuzzy variables and justify the use of P as an input In the special case P =0,Le.,the optimal threshold value should be:The process of fuzzy control is described as follows: In every decision...