Description of Traffic in ATM Networks by the First Erlang Formula

Transcription

1 5th International Conferene on Information Tehnology and Appliation (ICITA 8) Deription of Traffi in ATM Network by the Firt Erlang Formula Erik Chromý, Matej Kavaký and Ivan Baroňák Abtrat In the paper we deal with the poibility of the t Erlang formula utilization in Aynhronou Tranfer Mode (ATM) network. Thi tatement i poible on the bai of reearh of tatitial feature of traffi oure input flow. We onider ATM network type where in the ae of Virtual Path important parameter are lo, link utilization and The evidene of the t Erlang formula utilization in aynhronou network i ahieved through the model of video oure traffi. We have ued the direte Markov hain to reate the video oure traffi. Index Term-- Traffi deription, The Firt Erlang formula, Markov model, video oure model. I. INTRODUCTION It i obviou that with the help of the t Erlang formula, where uh parameter a lo B, link utilization and bandwidth rie, we are able to deribe the traffi in ynhronou network. On the other hand, to deribe the traffi in aynhronou network of Aynhronou Tranfer Mode (ATM) network type Markov hain [], [], [9], [] are often ued. But their diadvantage i that they are very ompliated and at the ame time they demand ompliated etimation. Paper [3], [] alo deal with the idea of the utilization of t Erlang formula. A in the ae of ATM network the optial fibre i ued a tranmiion medium, it i poible to onider ATM network to be network with low loe. Network with low loe are haraterized by the t Erlang formula, whih expree the onnetion lo probability in virtual path (VP) [5], []. The quetion if the utilization of the t Erlang formula i poible in aynhronou network roe from thi tatement. In thi paper we are going to deal with the reearh of the utilization of the t Erlang formula in aynhronou network. Thi work wa a part of reearh ativitie onduted at Slovak Tehnial Univerity Bratilava, Faulty of Eletrial Engineering and Information Tehnology, Department of Teleommuniation, within the ope of the projet VEGA No. /38/ Traffi in onvergent teleommuniation ytem and network. Erik Chromý i with the Faulty of Eletrial Engineering and Information Tehnology, Slovak Univerity of Tehnology, Ilkovičova 3, 89 Bratilava, Slovak Republi (telephone: , erik.hromy@tuba.k). Matej Kavaký, i with the Faulty of Eletrial Engineering and Information Tehnology, Slovak Univerity of Tehnology, Ilkovičova 3, 89 Bratilava, Slovak Republi ( matej.kavaky@tuba.k). Ivan Baroňák i with the Faulty of Eletrial Engineering and Information Tehnology, Slovak Univerity of Tehnology, Ilkovičova 3, 89 Bratilava, Slovak Republi (telephone: ivan.baronak@tuba.k). ICITA8 ISBN: The t Erlang formula, whih i uitable for the reearh of it utilization in aynhronou network, i known in the following form: k! k = k! = B where repreent perentage utilization of link, i link bandwidth and B i link lo. In next hapter we are going to deal with the reearh of parameter dependenie B, and. II. DEPENDENCY RESEARCH AMONG PARAMETERS The aim i to etimate dependenie among B,, parameter on the bai of the t Erlang formula in uh a manner that alway one parameter will keep ontant ize and the dependeny among other two parameter will be oberved. Etimation are done on the bai of (). A.. Dependeny among the link utilization and bandwidth at ontant lo On the bai of t Erlang formula it i poible to get dependeny of link utilization from bandwidth independent at ontant lo B. Data are hown in Fig B = % B = 5 % bandwidth - [Mbit/] Fig.. Dependeny of link utilization from bandwidth of given lo. For the purpoe of omparion the dependeny of link utilization from bandwidth at lo % and 5% ha been () 58

2 etimated. From the Fig. it i viible that with the inreaing bandwidth it i poible to inreae the link utilization the way that lo i preerved. The narrower the lo requirement (i.e. parameter B get maller value), the le link utilization i poible. B.. Dependeny among the lo and link utilization at ontant bandwidth On the bai of the t Erlang formula we get the lo dependeny B from the link utilization at ontant bandwidth. Data are hown in Fig.. Etimation were done for the ontant bandwidth = Mbit/, Mbit/ and 5 Mbit/. From Fig. it i viible that with the inreaing link utilization for given bandwidth the lo inreae a well. Further it i viible that at the ame link utilization and at different value the lo i different. With the inreaing bandwidth at the ame link, utilization lo dereae. C..3 Dependeny among the lo and bandwidth at ontant link utilization On the bai of the t Erlang formula we get the lo dependeny B from the bandwidth at ontant link utilization. Reult are hown in Fig. 3. Fig. 3 how that at the ontant link utilization and inreaing bandwidth lo B dereae. Further it i viible that at the ame bandwidth and different utilization the lo i different. With the inreaing link utilization, lo inreae a well. III. EVIDENCE OF THE ST ERLANG FORMULA APPLICATION IN ASYNCHRONOUS NETWORKS WITH THE HELP OF VIDEO SOURCE MODEL The aim i to prove the poibility of the t Erlang formula utilization in aynhronou network on the bai of imulation with the help of deigned mathematial model. There were parameter from real video oure ued during the reation of model for video traffi oure, whih i hown in [7] for video Ie Age DVD. On the bai of the method hown in [8] parameter neeary for the video oure model reation are etimated a follow: Tranition matrix P = [ p ij ], Size vetor of video oure model =...,. M tate [ ], Where M expree number of tate in Markov hain and,..., M video oure model tate are repreenting rate of ell generation. A the reult we have video oure model for M= P = = Mbit/ = Mbit/ = 5 Mbit/ link utilization = 95 % link utilization = 9 % link utilization = 8 % link utilization = 5 % Fig.. Lo dependeny from the link utilization at ontant bandwidth - [Mbit/] Fig. 3. Lo dependeny from the bandwidth at ontant link utilization. 59

3 3 =.873 kbit / = 75.7 kbit / = kbit / = kbit /. 5 = 89.9 kbit / =.9 kbit / = kbit / For the purpoe of imulation neeary imulation model oniting of ATM node without buffer tore and with video traffi oure [], [] on input of ATM node ha been reated. Input video traffi oure have different requirement from the point of view of bandwidth, lo and link utilization. There i an output link on the other end of ATM node, whih ha parameter defined a follow: bandwidth, lo requirement and link utilization. All thee parameter were adjuted aording to requirement temming from requirement of partiular ituation. A. 3. Dependeny among the link utilization and bandwidth at ontant lo Dependeny of link utilization from bandwidth (5 kbit/, kbit/, 5 kbit/, 8 kbit/ a 9 kbit/) at ontant lo B ( % a 5 %) ha been imulated. Reult are reorded in table and Fig.. Table and Fig. verify that with the inreaing bandwidth it i poible to inreae link utilization the way that lo i preerved. The narrower the lo requirement, the le link utilization i poible. Table : Dependeny of link utilization from bandwidth for given lo. B [%] B [kbit/] [%] [%] [kbit/] [%] Table : Lo dependeny from link utilization at ontant = 5 kbit/ =. Mbit/ =.8 Mbit/ [%] B [%] [%] B [%] [%] B [%] B. 3. Dependeny among the lo and link utilization at ontant bandwidth Dependeny of lo B from link utilization at ontant bandwidth = 5 kbit/, kbit/ and 8 kbit/ ha been imulated and reult are reorded in table and Fig B = % B = 5 % bandwidth - [kbit/] Fig.. Dependeny of link utilization from bandwidth of given lo. 8 = 5 kbit/ = kbit/ = 8 kbit/ Fig. 5. Lo dependeny from link utilization at ontant It i obviou that with the inreaing link utilization for given bandwidth the lo inreae a well. Further it i viible that with the ame link utilization and at different value the lo i different a well. With the inreaing bandwidth the lo dereae. 5

4 C. 3.3 Dependeny among the lo and bandwidth at the ontant link utilization Dependeny of lo B from bandwidth (5 kbit/, kbit/, 5 kbit/, 8 kbit/ a 9 kbit/) at ontant link utilization ha been imulated. Reult are hown in Fig.. 8 link utilization = 95 % link utilization = 9 % link utilization = 8 % link utilization = 5 % bandwidth - [kbit/] Fig.. Lo dependeny from bandwidth at the ontant link utilization. Fig. verifie that at ontant link utilization and inreaing bandwidth the lo dereae. Further it i viible that with the ame bandwidth and different link utilization the lo i different. With the inreaing link utilization the lo inreae a well. IV. DISCUSSION OF RESULTS Following tendenie were hown with the help of t Erlang formula: with the inreaing bandwidth it i poible to inreae link utilization the way that the given tranfer path lo i preerved, at ontant bandwidth and inreaing link utilization the tranfer path lo inreae a well, at ontant link utilization and inreaing bandwidth the tranfer path lo dereae On the bai of imulation with the help of deigned mathematial model of video oure model (built-up with the help of Markov hain) lited hange gained by the t Erlang formula have been verified. Thi i proved by table and diagram. In the ae of dependenie among tranfer path lo and link utilization at ontant bandwidth jut a mall differene ourred. It i obviou from the omparion of Fig. and Fig. 5. In the ae of etimation with the help of the t Erlang formula udden lo growth at maller bandwidth ourred, wherea in the ae of mathematial video oure model jut progreive growth of tranfer path lo with progreive growth of link utilization ourred. Conequently, imulation reult verified poibility of the t Erlang formula utilization alo in aynhronou network, where uh parameter a lo, bandwidth and link utilization are taken into onideration. V. CONCLUSION Nowaday we witne udden development in teleommuniation field. Converged tehnologie and onvergene proee are extremely attrative topi. Convergene repreent evolution path of with from atual teleommuniation to future modern multimedia teleommuniation infratruture for landline a well a for mobile network. Next generation network (NGN) are reult of onvergene. There exit everal important field within the frame of NGN matter, whih draw a lot of attention of profeional from the teleommuniation field. We peak about improvement of QoS parameter, management ytem, multimedia, routing matter in NGN network, dimenioning of network, optimization of ytem omponent of NGN platform and many other. It i beoming more viible, that the matter of network dimenioning in aynhronou network an be reearhed with the help of the t Erlang formula. On the bai of imulation with the help of video oure model the perpetive of the t Erlang formula utilization in aynhronou network ha been demontrated. All reult gained with the help of the t Erlang formula and video oure model are viible from diagram, whih prove thi tatement by evidene. REFERENCES [] Zhang, X., Shin, K.: Markov-Chain Modeling for Multiat Signaling Delay Analyi. IEEE/ACM Tranation on Networking, vol., Augut,, pp [] Bolh, G., Greiner, S., Meer, H., Trivedi, K.: Queueing Network and Markov Chain, Modeling and Performane Evaluation with Computer Siene Appliation. Seond Edition, John Wiley & Son, In., Hoboken, New Jerey,, ISBN-: [3] Fernandez, J., Mutka, M.: A Burt-Oriented Traffi Control Framework for ATM Network. Proeeding of the th International Conferene on Computer Communiation and Network, 995, pp [] Croetti, P.: Free Bandwidth for the Tranport of Connetionle Traffi Generated by Web Interative Multimedia Appliation and Servie. ITALTEL Central Reearh Lab, Milan, April, 99. [5] Chmelíková, Z.: Metody dimenzovania ATM ietí, prípevok na. eminari EaTT v Otrave, November, 999, ISBN X. [] Chmelíková, Z.: Analýza účanýh metód dimenzovania, prípevok na. eminári EaTT v Otrave, November,, ISBN [7] Video Trae for Network Performane Evaluation, Arizona State Univerity, [8] Roe, O.: Traffi Modeling of Variable Bit Rate MPEG Video and it Impat on ATM Network, Bayerihe Juliu-Maximilian-Unveritat Wurzburg, 997. [9] Sott, S., Smyth, P.: The Markov Modulated Poion Proe and Markov Poion Caade with Appliation to Web Traffi Modeling. Bayeian tatiti 7, Oxford Univerity Pre, 3. 5

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