Zamana bağlı trafik akışının modellenmesi ve dinamik yöneltme

Abstract

Yeni hat bağlaşmalı sistemler klasik elektromekanik merkezlere göre trafiği düzenlemede daha büyük esneklik sağlar. Bunun nedeni on-line veri isleme, trafik ölçmelerinin çeşitliliği ve tekrar programlanabilen trafik kontrolüdür. Son yıllarda zamana bağlı trafik akısı ve dinamik yöneltme konusunda bir çok çalışma yapılmaktadır. Yeni kontrol yeteneklerine uygun trafik modellerinin eksikliği, trafik mühendislerini daha iyi trafik modelleri oluşturmaya yöneltmiştir. Bu tezde, 10 sn gibi kısa çevrim uzunluklarında trafik ölçmelerini güncelleştiren ve onları şebekenin anlık yükünü dengeleyecek şekilde trafiğin güzergahını tekrar belirlemede kullanılan modeller çıkartılmıştır.

Several meanings can be assigned to the notion of time-dependent traffic. They can be clarified by- consider an infinite size trunk group with offered traffic p(t), arrival intensity A(t), and mean holding time 1/u : ji(t) = A(t)/u. In the stationary offered traffic, when calls arrive or are terminated instantaneous changes of the number of trunks busy are observed. The observation time scala in that case must be of order of 1 /A - In the stationary system, the mean and variance of number of trunks busy remain constant. Also in nonstationary offered traffic, the arrival intensity X depends on time: A = A(t), instantaneous state of trunk group can be observed. However, in this case the mean number in the system also evolves in time. Two different situations are possible : (a) change in offered traffic is abrubt ; (b) offered traffic changes slowly. The first situation is illustrated in Fig. 1. It is assume that the traffic starts to be forwarded to the empty system with fixed rate A. In this case the mean number in the system evolves on the time scale of order of 1/u, as contrasted to the time scale 1/uof intantaneous traffic fluctuations. -Ill- TRAFFIC Offered Traffic Mean Number Of Trunks Busy Intantaneoua Number Of Trunks Buay TIME Fig. Traffic Fluctuations In Fig. 2 more realistic patterns of changes in offered traffic are shown. There are two cases: (a) dynamic traffic flow, and (b) quasi-stationary traffic flow. The traffic flow is dynamic if the offered traffic changes so quicly that there is a significant phase shift between the peaks of mean offered traffic and the mean number of trunks busy, it is seen in Fig. 2a. The traffic flow is quasi-stationary if that phase shift is not observed, Fig. 2b. Traffic Traffic Offered Traffic if ^Carried Traffic (a) Fig. 2. Time Offered Traffic Carried Traffic Cb) Time a) Dynamic Traffic Flow b) Quasi-stationary Traffic Flow -IV- This situations can be related to traffic measurements. In modern SPO switching exchanges the following on-line measurements can be taken on each trunk group :. x(tn): number of trunks busy at time tn. ? Um(t") : number of calls connected between tn-i and t". Uout(tn): number of calls terminated between tn-x and t" At = t"-tn-i is the measuring cycle length the obvious conservation equation which hold3 both for the stationary and non-stationary traffic is : x(t"-i> = x(t"> +Uj.» - Em(t)]a (3) where Pu(t) is the blocking probability on the primary group and a(t) is the offered traffic (the parameter of the nonstationary poisson process). M(t,2) is the second factorial moment for the number of busy circuits in the overflow group. Calculation of m(t) using (2) is impossible as no exact formula is yet known for PN(t) with a=a(t). However, for a=c, a constant, exact PN(t) can be derived. Conseguently computation of v(t) using (3) is also a problem, but with the added complication in the form of M(t,2). Computation of M(t,2) involves the solution of (N+l) partial differential eguations ; not an easy task, especially when N is large, as the case in real-life systems. It is also assumed that the expectation of the holding times is constant and is normalized to one. For the case when this expectation is time-dependent, rescaling of the time-axis using a simple transformation enable the theory developed for unit mean holding time to be used. Next, the models A,B and C are designed so as to meet reguirement of on-line traffic measurements and control in modern SPC switching centers. The model A for random variable yn+i is obtained as follows. yn+± = a^Xn + bi'Un+i + W"+i (4) Where W"*i denotes a noise having the zero mean EE W^-m ] =0 and the coefficients ai and bx are given by 1 at = -El - exp(-T)] (5a) 1 1 bi = -El - ? El-exp(-T) ]> (5b) -VI- The model B for random variable x"+i is obtained x"*i = aa-x» + ba-U"+i + V"*i (6) The coefficients aa and ba are defined aa follows aa = exp(-T) (7a) 1 ba = -[1 - exp(-T)] (7b) T Thus, the model B has a linear structure as well as and differs from the model A in coefficients only. Model B adds little conceptually as companed to model A.