Erlang Formulas and Next Generation Networks

Transcription

1 Erlang Formulas and ext Generation etworks Erik hrom Department of Telecommunications, Faculty of Electrical Engineering and Information Technology Slovak University of Technology ratislava, Slovak Republic bstract The paper deals with the possibility of the Erlang and Erlang formula utilization in ext Generation etworks (G). ased on the common properties of synchronous and asynchronous networks it is possible the utilization of Erlang formulas also for asynchronous networks. It is possible to describe traffic in G networks by calculation of following parameters loss, link utilization and bandwidth. Keywords-Erlang formula; Erlang formula; ext Generation etworks; QoS I. ITRODUTIO Much attention is focused on description of traffic in asynchronous packet networks (represented by TM and IP networks). There are various methods for traffic description. Many of them are complex with high computational requirements. The description by Markov chains is one of them. Therefore the Erlang formulas can be very efficient and simple way how we can describe traffic parameters in asynchronous networks. Erlang formulas use traffic parameters such as loss, probability of delay, bandwidth and link utilization. These parameters are especially important from the Quality of Service (QoS) [8], [10] providing point of view. Hence the Erlang formulas seem to help us in the field of Quality of Service in ext Generation etworks (G). This paper focused on TM and IP networks [7] today used mainly as backbone networks for G. Erlang theory is described in detail in [3], [4], [13], [16]. II. TM ETWORKS synchronous Transfer Mode (TM) was the emerging network technology in the beginning of 90-ties. The main reasons for TM development were: Increasing demand for telecommunication and information technologies and services. onvergence of data and voice communication. TM networks are connection oriented networks. TM technology combines fast packet transfer with synchronous transfer through virtual circuits and virtual paths. It is cell switching mode which offers low transfer latency with high level of Quality of Service and ensures the support for voice, data and video service with high transfer rates. III. IP ETWORKS etworks based on Internet Protocol (IP) provide datagram service. IP transfer is non-connection oriented and its main feature is that it is best effort service. It means that the packet will be transferred in the best way, without forced delay and without unnecessary packet losses. The transfer of IP datagrams is done without guarantee of packet delivery [2], [6]. Services such as voice and real-time video are very sensitive on particular traffic parameters. The main of these parameters are delay, loss and error rate. We have to note that various types of services have also different bandwidth requirements. Therefore there is need for guarantee of these parameters. This guarantee is called Quality of Service. QoS requirements are: end-to-end delay, jitter, packet losses, bandwidth, link utilization. IV. ERLG FORMULS Two Erlang formulas ( and ) are used to describe the traffic in asynchronous networks. alculations were performed in Matlab environment.. The Erlang Formula The Erlang formula represents the ratio of lost calls. Therefore it is sometimes called loss Erlang formula. It is defined as follows:! 1 k 2 3! 1 k! 2! 3!! k 0 where: - ratio of lost calls [%], - total offered traffic [Erl], - number of channels (links). The first Erlang formula can be written also in the following form: 17

2 1 m k k 1 The use of the equation (2) can significantly decrease the computational requirements and we can also calculate the load of the system with the higher values [3, 4]. The following conditions must be met for the first Erlang formula: The flow of requests (calls) originates randomly with exponential distribution of incoming requests, which means the higher distance between requests, the lower number of these cases. Service time has similar distribution, i.e. exponential decreasing of requests with higher service time. The flow of requests is steady, as if it comes from infinite number of request sources. There is full availability of requests to all served links. Rejected requests do not return to incoming flow, therefore there are not repeated requests. o two requests will originate together [3]. IP traffic brings radical changes into telephone networks. The condition 2 is not fulfilled. nd because the traffic from one source is considerable increasing, also the condition 5 can not be met.. The Erlang Formula The Erlang formula also assumes infinite number of traffic sources. These sources generate the traffic for lines. The incoming request is inserted into waiting queue if all links are occupied. Waiting queue can store infinite number of requests concurrently. This Erlang formula calculates probability of creation of waiting queue in the case of traffic, and if it is assumed that the blocked calls will remain in the system until they are served [3].! where k 1 k 0 k!! where: - total offered traffic [Erl], - number of channels (links), - probability of waiting for service. The Erlang formula (3) can be simplified through following modifications: Dividing numerator and denominator by k0 k! consecutive use of Erlang equation (1). ( 1 ). ommon haracters of synchronous and Synchronous etworks Erlang formulas were primary intended for traffic description in synchronous networks. The idea is to use these formulas also for asynchronous networks. Synchronous network Lost calls [%] ratio Probability of waiting for service Total [Erl] offered traffic umber of channels (links) synchronous network Loss rate [%] Probability of delay [%] [Mbit/s] Link utilization andwidth Probability of delay for asynchronous networks represents the latency which occurs during transmission in the case of the heaviest traffic. This delay occurs in IP networks due to waiting queues in buffers in network nodes. Unfortunately, there is no similar parameter for jitter in synchronous networks, hence through Erlang formulas it can not be estimated. V. RESULTS FOR ERLG FORMUL This part represents results obtained by calculations through Erlang formula. Input parameters were given as follows: One of parameters is constant. Other parameter was increased in given step sequence. It is known that we can calculate the loss through Erlang formula if we have given link utilization and bandwidth. ut it is also possible to calculate the link utilization by method of bisection, if we know the bandwidth and loss [4].. andwidth and Loss in the ase of onstant Link Utilization The loss is decreasing if the bandwidth is increasing and link utilization is constant. The loss is increasing if the link utilization is k 18

3 . Link Utilization and Probability of Delay in the ase of onstant andwidth OSS In the case of constant probability of delay and increasing bandwidth the link utilization can be higher. In the case of constant link utilization and increasing bandwidth the probability of delay is decreasing. In the case of increasing link utilization and constant bandwidth the probability of delay is D DT Figure 1. Dependency between loss and bandwidth in the cases of constant link utilization.. The Loss and Link Utilization in the ase of onstant andwidth P O T OF D UT TO OSS Figure 3. Probability of delay in the case of constant bandwidth and increasing link utilization. UTU TO Figure 2. Dependency between loss and link utilization in the cases of constant bandwidth. y increasing link utilization the loss is also increasing if the bandwidth is constant. y increasing bandwidth the loss is decreasing if the link utilization is constant. VI. RESULTS FOR ERLG FORMUL This part represents the results obtained by calculations through Erlang formula (4). y this equation we can calculate the possibility of delay and loss if we know the two parameters the link utilization and bandwidth. lso in this case the input parameters were given as follows: One of parameters is constant. Other parameter was increased in given step sequence.. Link Utilization and andwidth in the ase of onstant Probability of Delay y use of the Erlang formula (4) and the method of bisection is possible to obtain the dependency of the link utilization if the probability of delay is constant and bandwidth is The results are depicted in the Fig. 4. In the case of constant link utilization and increasing bandwidth the probability of delay is decreasing. In the case of constant bandwidth and increasing probability of delay the link utilization is In the case of increasing bandwidth and constant probability of delay the link utilization is 19

4 UT T O P O T OF OSS D DT Figure 4. Link utilization in the case of constant probability of delay and increasing bandwidth. UT TO D DT Figure 6. Dependency between loss, bandwidth and link utilization.. Probability of Delay and Loss if the Link Utilization and andwidth are changing y use of the Erlang formula (4) is possible to obtain dependencies of probability of delay and loss if the bandwidth and link utilization were changing. The obtained results are shown in the Fig. 5 and 6. In the case of increasing link utilization together with decreasing bandwidth the loss and probability of delay are In the case of constant bandwidth together with increasing link utilization the loss and probability of delay are In the case of constant link utilization together with increasing bandwidth the loss and probability of delay are decreasing. VII. RESULTS FOR ERLG FORMUL The paper proposes the idea of utilization of Erlang and Erlang formulas for description of traffic in G networks. ll obtained tendencies through the calculations suggest the possibility of the Erlang formulas use in G networks (transport layer is represented through the TM or IP network). Erlang formula does not contain parameter for probability of delay, therefore this formula is more suitable for TM network, because the probability of delay in this network is omissible. Through the Erlang formula is possible to estimate the probability of delay, which usually occurs in IP networks. Description of traffic gives the opportunities to monitor the Quality of Service parameters in G networks. It seems that simplicity and unpretentiousness of Erlang formulas can be their strong advantage against other methods for traffic description in asynchronous networks, but the more future research is necessary in this field. P O T OF D KOWLEDGMET This work is a part of research activities conducted at Slovak University of Technology ratislava, Faculty of Electrical Engineering and Information Technology, Department of Telecommunications, within the scope of the projects VEG o. 1/0565/09 Modelling of traffic parameters in G telecommunication networks and services and the partial result of the Research & Development Operational Programme for the project Support of enter of Excellence for Smart Technologies, Systems and Services, ITMS , co-funded by the ERDF. D DT UT TO Figure 5. Dependency between probability of delay, bandwidth and link utilization. REFEREES [1] MULLER,. J.: Desktop Encyclopedia of Telecommunications. Edition: 3, McGraw-Hill Professional, 2002, IS [2] PUŽMOVÁ, R.: Modern communication networks from to Z. omputer Press rno, 2006, IS [3] KLIK, O.: Theory and experience of operation load in telecommunications. Praha, 1973, OS

5 [4] OOPER, R..: Introduction to Queueing Theory: 2nd Edition, Elsevier, 1980, IS [5] KRUSE, M., TIPTO, H. F.: Information Security Management Handbook. Edition: 4, R Press, 1999, IS [6] TYLOR, T.: QoS in Packet etwork. Springer, 2004, IS [7] VOZÁK, M.: dvanced Implementation of IP Telephony at zech universities, WSES TRSTIOS on OMPUTERS, Issue 1, Volume 9, September 2010, ISS: , pp , [8] LOGH, T., MEDVEKÝ, M.: Performance nalysis of Priority Queuing ased Scheduling lgorithms. In: 33rd International onference on Telecommunications and Signal Processing - TSP 2010, ugust 17-20, 2010, aden near Vienna, ustria, pp , IS [9] HLÁS, M., KYRSHOV,., KOVÁIK, M.: Influence of Encryption on VoIP onnection Quality, In RTT Research in Telecommunication Technology: 9th International onference. Vyhne, Slovak Republic, , pp , IS [10] LUKÁROVÁ, D., MEDVEKÝ, M.: Investigation of -RIO, RnRED and WRED algorithms from the point of QoS support. In: 33rd International onference on Telecommunications and Signal Processing - TSP 2010, ugust 17-20, 2010, aden near Vienna, ustria, pp , IS [11] QIO, S. Robust and Efficient lgorithm for Evaluating Erlang Formula. Hamilton, Ontario anada : McMaster University, [12] Diagnostic Strategies. Traffic Modeling and Resource llocation in all enters. : eedham (Mass., US) : Diagnostic Strategies, [13] Westbay Engineers Ltd. The Extended Erlang Traffic Model. : Westbay Engineers Ltd., ng_b_traffic_model.htm [14] FREEM, R.: Fundamentals of Telecommunications, Second Edition. John Wiley & Sons, Inc. Hoboken, ew Jersey, IEEE Press, 2005, IS [15] KVKÝ, M., ZOLY,.: IP Videokonference in Learning Process. In IET 2010 : 8th International onference on Emerging elearning Technologies and pplications. Stará Lesná, Slovakia, Košice: Elfa, 2010, s IS [16] MIŠUTH, T., ROÁK, I.: Performance Forecast of ontact entre with Differently Experienced gents. In: Elektrorevue Electrotechnic magazine, 2010/ , pp , ISS