Hibrit bağlaşmalı şebekeler için performans modelleri

Abstract

Hibrit bağlaşma; devre ve paket bağlaşmanın birlikte kullanılmasına imkan veren bir tekniktir. Bu tekniğin kullanıldığı bir ortamda, çağırma ve veri olmak üzere temelde iki farklı trafik grubu vardır. Hibrit bağlaşmalı bir yapının performans modellemesi, bu iki farklı trafik grubu arasındaki etkileşimden dolayı teletrafik teorisi açısından değişik bir uygulamadır. Bu çalışmada, çeşitli hibrit bağlaşma yapılanım ilişkin performans modelleri incelenmiştir. Tüm modellerde, ilk önce ele alınan yapının özellikleri ortaya konduktan sonra yapılan analizler sayesinde sistemin en önemli performans parametreleri olan çağırmaların blokaj olasılığı, PB, ile paketlerin ortalama zaman gecikmesi, E(T), ifadeleri bulunmuştur. Daha sonra bulunan ifadelerin doğruluğundan emin olmak için ele alınan yapıların eşdeğerlerine veya limit durumlarına göre kontroller yapılmıştır. Son olarak da eşdeğer ayrı sistemlerle ve diğer hibrit bağlaşma yapılarıyla karşılaştırma yapmak, iki grubun birbirinin performansı üzerindeki etkisini görmek ve incelenen hibrit sistemin genel olarak performansım düzeltme yolları önermek amacıyla bulunan sonuçlar üzerinde yorumlar yapılmıştır. Bu çalışmada hibrit bağlaşmak yapılar sadece performans modellemesi açısından ele alınmıştır. Bununla birlikte, hibrit bağlaşmanın ana hatlarına ve kullanılan çoğulîama düzenine aynııtılı olarak 2. Bölüm'de yer verilmiştir. İncelenen modellerin tümü SENET tipi hibrit bağlaşmak yapılara aittir. Her iki gruptaki tüm hizmetlerin aynı hızda oldukları kabul edilmiştir. Erişim imkanı bulunmadığında çağırmalar bloke edilmekte; paketler ise kuyruğa alınmaktadır. Sürekli zamanda yapılan modellerdeki analizlerin çoğunda tam analiz yöntemi kullanılmıştır. Bu çalışmanın amacı, tek başlarına davranışları daha önceden bilinen iki farklı trafik grubunun çeşitli hibrit bağlaşma yapılarındaki performanslarının ne olacağını bulmaktır.

In this study, performance models for various SENET (Slotted Envelope Network) type of hybrid switched structures are investigated. Hybrid switching is a technique (scheme) which enables simultaneous circuit and packet switched services to be provided in the same network. It is considered as a third switching method which combines the features of two switching techniques within the single environment. Performance modeling of hybrid switching is a very interesting application from the teletraffic theory point of view, because of the interaction between circuit and packet switched traffic. Hybrid switching can be usually used among some common nodes of the seperated circuit and packet switched networks belonging to the same communication authority; in integrated networks like ISDN; in local networks and mobile communication, both of which contain voice and data services. It is apparent that circuit and packet switching are two different modes of handling traffic. So, first of all, these two techniques had moved closer together and then hybrid switching idea arised in the middle of 1970s. After basic concepts of hybrid switching were described, models were developed to evaluate the performance of hybrid switched systems. These modeling studies were being encountered between 1978 and 1986 (esp. 1983-1985) the most frequently. Although these studies have plunged since 1990 due to a great popularity of ATM (Asynchronous Transfer Mode) for last years, they have still continued nowadays. The aim of this study is to examine the performance of circuit and packet switched traffic, which were already modeled seperately, for various basic hybrid switched structures. This study is organized as follows. Chapter 1 is an introduction. Chapter 2 gives the basic concepts of hybrid switching and some preliminaries required during the modeling. In Chapter 3, we examine two simple models for a sing le channel hybrid switching scheme using the second type of frame structure: VI the FCFS (First Come First Service) strategy and one in which the voice calls have preemptive priority over the packets. Chapter 4 presents two different models for the movable boundary scheme: Ni=N2=l channel case and one, which has unrestricted number of channels, works in the underload region. In this chapter, we besides handle the necessity of using a flow-control mechanism which prevents from penetrating the overload region; utilization voice silence periods and a modeling method for this case. In Chapter 5, we together evaluate the results of all models and explain the usage of hybrid switching in today. Appendix A gives general information about moment gene rating functions which is frequently used for numerical solutions in this study. II. THE BASIC CONCEPTS Traffic Groups and Integration: There are basically two different traffic groups in a hybrid switching system. The first and second groups contain the services requiring circuit and packet switching, respectively. It is possible that there are various services with different rates in the same group, because these services are grouped according to their switching techniques. In spite of this real situation, it is assumed that all services in the same group have the same rate for simplicity and comparability of developed models. So, the first and second groups are frequently called as voice (call) traffic and data (packet) traffic, respectively. Consequently, hybrid switching systems, for which performance models are developed, are considered as though they only consist of two different traffic types, voice and data. In this study, all services in both groups are the same rate. Hybrid switching can be perceived as an integration method which combines voice and data traffic, usually provided by seperated networks, in the same structure. In this case, hybrid switched systems have some advantages, such as using the communication facilities (especially transmission and switching) more efficently and economically than seperated networks. Multiplexing Scheme: hi hybrid switched systems, Time-Division Multiplexing (TDM) is used. The basic idea of this scheme is to multiplex two different traffic groups over the same transmission medium together and thus to be shared out the high capacity between two groups dynamically. Frame Structure: In hybrid switched systems, two kinds of frame structure are used. 1)A frame of N slots is divided into two distinct sections by means of a boundary. The first section, containing Nx slots, is allocated to the calls. The second sections, with N2:=N-N1 slots, is reserved for the data packets. 2)A frame is handled as a whole instead of two distinct sections. In this structure, all slots in a frame can be used by both groups. Vll Basic features of both frame structures are listed as follows: l)The transmissi on capacity is partitioned into frames, each frame is further decomposed into time slots like all TDM structures. 2)The frame length (time), which is d seconds, is fixed for all frames in order to provide synchronization and message continuity. 3)Choosing the Slot Size: The slot length only depends on its owner's rate, since d is fixed. Thus, whether users have the same rate is an unique criterion in order to determine the slot size. We assume that all users have the same rate so all slots in a frame have the same size for both frame structures. 4)Slot Allocation to the Groups: For the first frame structure, at the beginning of the frame period, voice calls are loaded into their slots in section- 1 in the order of arrival. Queued packets are then placed into their slots. For the second frame structure, an incoming message is directly loaded into the frame without taking into consideration call or packet. An unique slot from every frames is assigned to each user due to the equality of all user's rates. 5)The features of the frame format used in this study are: T-l carrier or 23B+D interface of ISDN is used as a digital transmission path. Both capacities are 1.544 Mbps. The frame length is 1/8000=125 jxsec (193 bits) which is the same as voice digitization rate. The length of all slots is 8 bits and thus there are 24 slots in a frame. One bit remaining in every frames is used for synchronization. This frame format is appropriate for both frame structure under the assumption that all users have the same rate. Boundary: hi the first frame structure, there are two different boundary cases. 1) Fixed Boundary: The boundary position and the number of the slots used by both groups are the same for every frames. It is considered that the system is divided into two independent subsections and thus the capacity is not dynamically shared between groups. Each group can only use its own slots. 2) Movable Boundary: The boundary moves towards the section- 1. Voice calls again use their own slots. Data packets use not only their own slots but also free voice slots. Let N^t), 0< Nı(t) < Nls denote the number of slots occupied by calls during the t th frame. Then, N-Ni(t) slots are made available within the t th frame for the transmission of packets. An arriving call is allowed to preempt a packet occupying one of its allocated slots, if all Ni slots are busy. The movable boundary strategy allows for a dynamic sharing of transmission capacity between groups and increases the efficiency of resource usage, because it enables the packets to utilize idle voice capacity. The Key System Performance Parameters: In hybrid switched systems if there are not any channels for service, voice traffic is blocked and packet traffic is queued. So the key system performance parameters are the probability of loss for calls, PB, and the expected time delay for packets,E(T). Vlll Analysis: Two distinct analysis domains are available the integration voice and data traffic onto a TDM frame. One is discrete-time analysis, in which the slot structure is explicitly accounted for in the analysis. Another is continuous-time analysis, which ignores the discrete slots of the TDM frame and focuses on the concept of channels only. It is a valid, if the frame length is small compared with the service time required to transmit both groups. For our frame format, the frame length, 125 usee, is much shorter than 18.75 msec, the service time of a data packet 1200 bits long, and the call holding time lasting several minutes. So, we use continuous-time analysis. In continuous- time, the discrete nature of the TDM frame can be neglected and one slot of 8 bits every 125 usee corresponds to 64 kbps transmission capacity. In essence, with continuous-time analysis we assume that N=24 channels, all of which have the same 64 kbps capacity, operate in parallel. Several analysis methods are available to find closed-form expressions for PB and E(T). These methods will not be necessary, unless there is an interaction between groups. Because, the traffic which is not affected by the other group would be modeled, as if it were alone. In hybrid switching systems, in general only packet traffic is affected by voice traffic. E(T) is thus found by one of the analysis methods listed below. 1) Exact Analysis: Analysis is directly performed according to real operation of the system without any assumption. It will be a valid method due to numerical difficulties, only if there are a few number of channels. 2) Approximative Analysis: Analysis is performed under the assumptions made in accordance with the structure of the system. There is no restriction about the number of channels, so this method is mostly used for larger systems. There are several kinds of approximative analysis methods such as fluid-flow, quasi-static, diffusion and decomposition approximations. The exact analysis method for a few number of channels is almost always used throughout this study. Although this method may not be considered as an appropriate method in practice because of restricted number of channels, it has some advantages as follows: 1)PB and E(T) are obtained by this method the most simply and clearly. 2)It is simple to interpret PB and E(T), so we can easily see that how each group affects the other's performance; performance of each group is compared with its equivalent seperated system (the equivalence of one group is found to be supposed that other group is absent); PB and E(T) can easily be checked with respect to call and packet equivalances and limit cases. 3)The interpretions made according to PB and E(T) found by this method is independent of the number of channels. 4)PB and E(T) obtained by this method usually have good references for approximative analysis. Common Features: In addition to ones mentioned earlier, other common features which are valid for all models in this study are listed as follows: l)The IX data queue, with FIFO discipline, has infinite buffer capacity. 2) Voice and data traffic are modeled by a Poisson arrival process of the rate %1 and X2, respectively. They also have negative exponential service time distribution witii the parameter I/U4 and l/u,2 > again respectively. 3)Analysis is performed for steady state of system, all probability expressions are thus independent of time due to stationarity. 4)A11 hybrid switched structures are SENET type, which is the most frequently encountered and the oldest scheme of this area. III. MODELS FOR THE SECOND TYPE OF FRAME STRUCTURE In addition to common features, the characteristics which are valid for both models are listed as follows: 1) The second type of frame structure is used. 2) The hybrid switched scheme in this section has a single channel. The exact analysis method is thus used. 3) The voice and data equivalances of the hybrid switched scheme in this section are Erlang-B with single server loss system and M/M/l queue, respectively. Model Using The FCFS Discipline: A channel is assigned to either user in order of arrival. Voice arrivals will be blocked unless the channel is free. Data arrivals will be buffered in FIFO manner whenever the channel is occupied. The two-dimensional state space of hybrid switched systems is defined by the number i of calls in progress and by the number j of packets in the system. Transitions between states follow the pattern shown in Page 27 (for N=l channel, i=0,l andj=0,l,2..., with an infinite buffer size). i he balance equations written from tins state diagram can be solved by utilizing recursive ways, moment-generating functions and boundary equations. In the result, PB and E(T) are found as follows: pB=7^r (») Td ^^rV+rrrr T 1+Pi v / I- Pi 1+Pi Note: Defining Pı^/ji!, Çh^^Pı and letting a=(l/u.i)/(l/u,2) be the ratio of voice to packet service time. These parameters are always used in the expressions throughout this study. As a check, if we set p2=0 in Eq.(l) we get the Erlang-B blocking probability of a single channel case. With pi=0 for Eq.(2), one gets the M/M/l normalized time delay expression coming into view in Appendix Eq.(A.22). The effect of the queued packets competing with calls for the common channel is to increase the blocking probability. The only way to reduce PB substantially is to keep all traffic low. The second term of Eq.(2) represents the increase in the time delay in accordance with packet equivalance of the system. This increase is due to the competition with calls for the use of the common channel. In practice, a »1. The time delay thus increases enormously because of the a, which appears in the numerator of the second term in Eq.(2). In other words, it is not possible to improve the time delay by varying pi and p2 because of strongly dependence of a. The equilibrium condition for the data queue is p2<="" n2:="" a="" reasonable="" length.="" 2)overload="" n2="" :="" extra="" ordinarily="" long="" may="" result.="" movable="" boundary="" model="" ni="N2=l" channel:="" we="" take="" special="" case="" scheme="" n1="N2:=1" allocated="" each="" groups.="" exact="" analysis="" method="" is="" thus="" used.="" and="" equivalances="" this="" single="" server="" m="" l="" queue,="" respectively.="" all="" checkings="" performed="" pi-»0="" pi-»»,="" which="" limit="" cases="" system.="" looks="" like="" mm="" 2="" p!-="" style="margin: 0px; padding: 0px; outline: 0px;">oD (i=l) and Pi-M) (i=0), respectively. The voice calls under movable boundary conditions are thus not affected by data packets. The voice traffic blocking probability is precisely the Erlang-B expression with Ni servers, given in general case by Pb-ECp^NO^ 1/Ni' andforN^l Pb^t^T (8) 2,p!J/j! j=o We find u.2E(T) for two data traffic regions to be given by following two expressions by utilizing two-dimensional state diagram shown in Page 44. 1 ) In the Underload Region : a » 1 and p2 < N2= 1 4 p. 2) In the Overload Region : a » Î and p2 > N2= 1 (9.b) d. j -.«(Pa-1)^ V 2+p2 p2(l + Pl)2; The parameter "a" represents a measure of the average capacity remaining with total utilization p. hi general form a=N-p. For this model we have a = 2-p = 2-p2-T£- = l-p2+r-?- (10) 1+Pı 1+Pi As a check on Eq.(9.a), one gets the M/M/2 and the M/M/l average time delay expressions, appearing in Appendix (A31) and (A22), for the cases p!=0 and Pi->co, respectively. Moreover, as p2-»0 -i.e., data traffic is negligible- E(T) ->l/u.2 Just the packet service time, as expected. xni The blocking performance of calls is the same as fixed boundary case or call equivalance of the system, because there is not any effect from packets. Eq.(9.a) turns out to be independent of a. So, the time delay considerably decreases with respect to two models examined in the previous section. In the underload region, the time delay varies between M/M/l (the worst case, Pi-»») and M/M/2 (the best case, pi=0) and is always better than the data equivalance of the system. The time delay in the overload region, given by Eq.(9.b), however, is proportional to a. Since a »1 has been assumed in obtaining this result, it is apparent that the time delay increases rapidly as one attempts to penetrate the p2 > N2=l region by driving more data traffic into the system. In the movable boundary operation, data utilization (p2) may exceed the data system dedicated capacity of N2 slots/frame. This is correct. However, inordinately large queues are found to appear in the overload region. As a result, data traffic must always operate in the underload region and a flow-control mechanism for data traffic should be used with a movable boundary scheme to ensure that the overload region is not penetrated. Movable Boundary Model for the Underload Region: There is no restriction about Ni and N2 (Ni, N2 >1). An approximation procedure, which is valid under the continuous-time assumption only, is thus used. It is assumed that the movable boundary scheme always operates in the underload region. We obtain our approximation for the wait time, E(w), by making some observation. If the voice system were always operate in a state i, the number of channels available for packets would be N-i and the average wait time would be given by Erlang-C distribution. However, the movable boundary scheme does not always operate in only one state i. Instead the state of the occupancy mo^ values (0 < i < Ni). So, the wait time of the packets is found by averaging over the Erlang-C distributions of the various states. Finally, the normalized packet waiting time is obtained as follows : !*>E(w) = ıızZ P(i) E(w;) = i ZP(i) Ew(ft) (11), i=0 «. i=0 P(i) is the probability that the system is in state i and E2>N_j(p2), shown in Eq.(4.3 1), is the Erlang-C distribution with N-i server and p2 traffic utilization. As a check, for the special case Ni^N^l channel, analyzed in the previous subsection, Eq.(l 1) is reduced to the wait time obtained from Eq.(9.a). From Eq.(l 1), it is seen that fi2E(w) is inversely proportional to a. Since a is the number of free channels, which can be used by packets, it is a reasonable result. xiv Flow-Control for the Overload Region: The fluid-flow technique is usually used in order to model the operation in the overload region. The basic idea behind the fluid-flow approach is to model the data portion of the movable boundary system as a deterministic system and to model the queue-length distribution as a continuous process, with arriving flow X2 [packets/sec] and departing flow (N-i)p.2 [packets/sec]. Under this assumption, the net rate at which the data queue builds up with i voice calls in the system is then ri = X2-(N-i)^2 i=0,l,...,Ni (12) All parameters in Eq.(12) have already described. If r, > 0 or X2> (N-i)jj.2 the data queue will tend to increase linearly at this rate. If r; < 0 or X2< (N- \)\i2, the data queue will tend to decrease. In the overload region, as a result of the average values of i, rj can be less than 0. But it does not guarantee that there are no excessive agglomeration in the data queue permanently. If n > 0 with the increase of i even for a very short time interval, it will be clear that large excursion in the data queue-length is possible during this short time interval because of a »1. In this case, the movable boundary scheme should always operate in the underload region without penentrating to the overload region in order to obtain the maximum efficency from this scheme. For this reason, a flow-control mec hanism, which controls X2, can be used. When X2 has reached N2\x2, the limit value to enter the overload region, either following ways are used: 1) X2 is restricted. 2) The MB-2, enabling packets to utilize the voice silence periods, is used, i is thus decreased without reducing pi. Using the Voice Silence Periods: In the movable boundary scheme, free voice slots are obtained in two different ways : 1) The data traffic uses the voice slots remaining naturel voice calls containing silences as well as talkspurts. 2) The packet traffic uses not only idle voice calls but also additional slots acquired to be eliminated the voice silence periods. The voice traffic only consists of talkspurts. For these two types of movable boundary scheme we use MB-1 and MB-2 notations, respectively. For the MB-2, first of all, the silence and talkspurt sections in a voice call are distinguished to each other. This procedure is called as Digital Speech Interpolation (DSI) in the digital environment and is performed by Speech Activity Detector (SAD). The multiplexer employing SAD performs DSI as well as movable boundary functions. Since the MB-1 can not be completely used during the voice overload periods, it is possible that large data queues build up due to a »1. However, using the MB-2 improves the data performance, because it enables the packets to utilize voice capacity even during the voice overload periods. If it is taken into xv consideration that there are silences occuring as much as 60 percent of the time when a person is speaking, this improvement will be understood much easier. A scheme allowing the utilization of voice silence periods, of which packets do not make use in usual, can be used for both frame structures. V. CONCLUSION The results obtained from all models can be evaluated as follows : 1) All performance models related to hybrid switched systems are essentially developed for more general case, the integration of synchronous voice traffic and asynchronous data traffic. Voice and data are the most common and characteristic example of circuit and packet switching, respectively. So, it is considered that synchronous traffic is circuit switched and asynchronous traffic is packet switched. This consideration does not have any drawbacks from modeling point of view. Furthermore, it is usually valid in practice. Finally, these performance models can be applied to much more number of areas. 2) Why is hybrid switching, based on TDM, chosen for performance modeling instead of ATM, which has the great popularity nowadays? Because modeling of ATM traffic is much more difficult due to its inherent burstiness. 3) Some ways can be suggested in order to improve the system performance. 1) Voice Performance: It is not necessary to use a special scheme for the first frame structure. Calls must have preemptive priority over packets for the second frame structure. 2)Data Performance: The fixed boundary, MB-1 and MB-2 can be respectively used to obtain better data performance. There is no way to improve the packet performance except utilization voice silence periods for the second type of frame structure. Hybrid switching, whose performance modeling is minutely employed in this study, İs used in several areas as follows : l)LANs: The Hicom LAN CP ring consists of the circuit switched section containing PABXs and connection of remote switches and the packet switched section organized as a token ring as per IEEE 802.5. Both sections provide a transmission rate of 16 Mbps over a common fiber optic cable. IVDLAN interface, defined by IEEE 802.9, contains five channels. Two of them are B channel of ISDN; one is D channel of ISDN for signalling purpose; one is C channel for video interface and the last one P channel for a LAN interface. B and C channels are assigned to circuit switched services while D and P channels are used by packet switched services. 2)ISDN: Hybrid switching is used for 23B+D interface, which is the compatible with the 1.544 Mbps T-l standart. The 64 kbps B channel could be used for digital voice or circuit switched data; the 64 kbps D channel could be used for carrying packet switched data as well as control packets. xvi 3)Mobile Communication: Hybrid switching is used in the integrated TDMA mobile radio systems. In this system, voice traffic, whose performance measure has been given by Üıe M/M/C/C queueing model, is circuit switched and data traffic is packet switched using slotted ALOHA for channel access.