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; 614990, , . . 15; e-mail: erm6@mail.ru Fourth International Conference I.TECH 2006 Networks and Telecommunications DIMENSIONING OF TELECOMMUNICATION NETWORK BASED ON QUALITY OF SERVICES DEMAND AND DETAILED BEHAVIOUR OF USERS Emiliya Saranova Abstract: The aim of this paper is to be determined the network capacity (number of internal switching lines) based on detailed users behaviour and demanded quality of service parameters in an overall telecommunication system. We consider detailed conceptual and its corresponded analytical traffic model of telecommunication system with (virtual) circuit switching, in stationary state with generalized input flow, repeated calls, limited number of homogeneous terminals and losses due to abandoned and interrupted dialing, blocked and interrupted switching, not available intent terminal, blocked and abandoned ringing (absent called user) and abandoned conversation.

We propose an analytical - numerical solution for finding the number of internal switching lines and values of the some basic traffic parameters as a function of telecommunication system state. These parameters are requisite for maintenance demand level of network quality of service (QoS). Dependencies, based on the numerical- analytical results are shown graphically.

For proposed conceptual and its corresponding analytical model a network dimensioning task (NDT) is formulated, solvability of the NDT and the necessary conditions for analytical solution are researched as well. It is proposed a rule (algorithm) and computer program for calculation of the corresponded number of the internal switching lines, as well as corresponded values of traffic parameters, making the management of QoS easily.

Keywords: Telecommunication Network, Circuit Switching, Network Traffic, Terminal Traffic, Human Factors, Network Dimensioning.

1. Introduction The purpose of the teletraffic theory is to find relation between quality of services and equipment cost [Iversen 2004]. This is very important for a good planning and controlling of telecommunication networks.

The Quality of service (QoS) concept is defined in the ITU-T Recommendation E-800 as: The collective effect of service performance, which determines the degree of satisfaction of a user of the service.

QoS parameters are administratively specified in Service Level Agreement (SLA) between users and operators.

These QoS parameters (from a contract of SLA) are reflecting on GoS parameters.

Network dimensioning is necessary for designing and control of network and its level of quality of services (QoS), in an advance determined level.

Based on a given set of QoS requirements, a set of GoS (Grade of service) parameters are selected and determined as functions of human behaviour characteristics.

Networks and Telecommunications 2. Conceptual Model In this paper we consider detailed conceptual and its corresponded analytical traffic model [Poryazov 2005b] of telecommunication system with channel switching, in stationary state, with BPP (Bernoulli-Poisson-Pascal) input flow, repeated calls, limited number of homogeneous terminals and losses due to abandoned and interrupted dialing, blocked and interrupted switching, not available intent terminal, blocked and abandoned ringing and abandoned conversation.

The conceptual model of the telecommunication system includes the paths of the calls, generated from (and occupying) the A-terminals in the proposed network traffic model and its environment (shown on Fig. 1).

The names of the virtual devices used are constructed according to the device position in the model.

dem.Fa Fo (Nab+M Yab) Fo copy ed cd cs cr cc s inc.Fa ad id bs is ns br ar ac a Fb rad rid rbs ris rns rbr rar rac rcc STAGE:

dialling;switching;ringing; communication.

BRANCH EXIT: BRANCH:

Fb Generator;

r = repeated; e = enter Terminator;

cr cc t = terminated a = abandoned;

Modifier;

= not considered.

b = blocked; Server;

b Enter Switch;

i = interrupted;

ar ac Switch;

n = not available;

Fb Graphic Connector.

c = carried.

Virtual Device Name = Fig. 1. Normalized conceptual model of the telecommunication system and its environment and the paths of the calls, occupying A-terminals (a-device), switching system (s-device) and B-terminals (b-device); base virtual device types, with their names and graphic notation.

2.1. The Comprising Virtual Devices The following important virtual devices on Fig.1 are shown and considered:

a = comprises all the A-terminals (calling) in the system (shown with continuous line box).

b = comprises all the B-terminals (called) in the system (box with dashed line).

ab = comprises all the terminals (calling and called) in the system (not shown on Fig.1);

s = virtual device corresponding to the switching system. It is shown with dashed line box into the a-device.

Ns stand for the capacity (number of equivalent internal switching lines) of the switching system.

2.2. Stages and Branches in the Conceptual Model:

Service stages: dialing, switching, ringing and communication.

rep.Fa Fourth International Conference I.TECH 2006 Every service stage has branches: enter, abandoned, blocked, interrupted, not available, carried (correspondingly to the modeled possible cases of ends of the calls' service in the branch considered).

Every branch has two exits: repeated, terminated (which show what happens with the calls after they leave the telecommunication system). Users may make a new bid (repeated call), or to stop attempts (terminated call).

2.3. Device Parameters and its Notations in the Conceptual Model:

Letter F stands for intensity of the flow [calls/sec.], P = probability for directing the calls of the external flow to the device considered, T = mean service time, in the device, of a served call [sec.], Y = intensity of the device traffic [Erl], N = number of service places (lines, servers) in the virtual device (capacity of the device). In the normalized models [Poryazov 2001], used in this paper, every virtual device, except switches, has no more than one entrance and/or one exit. Switches have one entrance and two exits. For characterizing the intensity of the flow, we are using the following notation: inc.F for incoming flow, dem.F, ofr.F and rep.F for demand, offered and repeated flows respectively (ITU E.600). The same characterization is used for traffic intensity (Y).

Fo is the intent intensity of calls of one idle terminal; inc.Fa = Fa is intensity of incoming flow of A-terminals and M is a constant, characterizing the BPP flow of demand calls (dem.Fa). If M = -1, the intensity of demand flow corresponds to Bernoulli (Engset) flow model, if M = 0 - to the Poisson (Erlang), and if M = +1 - to the Pascal (Negative Binomial) flow model. In our analytical model every value of M in the interval [-1, +1] is allowed. The BPP-traffic model is very applicable [Iversen 2004], but in the numerical examples, presented here, M = 0, because the conclusions made are independent of the input flow model.

2.4. The Main Assumptions of the Model:

For creating a simple analytical model, we make the following system of fourteen (A-1 A-14) assumptions [Poryazov 2005b]:

A-1. (Closed System Structure) We consider a closed telecommunication system with functional structure shown in Fig. 1;

A-2. (Device Capacity) All base virtual devices in the model have unlimited capacity. Comprising devices are limited: ab-device contains all the active Nab [2, ) terminals; switching system (s) has capacity of Ns calls (every internal switching line may carry only one call); every terminal has capacity of one call, common for both incoming and outgoing calls;

A-3. (A-Terminal Occupation) Every call, from the flow incoming in the telecommunication system (inc.Fa), falls only on a free terminal. This terminal becomes a busy A-terminal;

A-4. (Stationarity) The system is in stationary state. This means that for every virtual device in the model (including comprising devices like switching system), the intensity of input flow F(0, t), call holding time T(0, t) and traffic intensity Y(0, t) in the observed interval (0, t) converge to the correspondent finite numbers F, T and Y, t when. In this case we may apply the theorem of Little (1961) and for every device: Y = FT ;

A-5. (Calls' Capacity) Every call occupies one place in a base virtual device, independently from the other devices (e.g. a call may occupy one internal switching line, if it find free one, independently from the state of the intent B-terminal (busy or free));

A-6. (Environment) The calls in the communication systems' environment (outside the blocks a and b in Fig. 1) don't occupy any telecommunication systems' device and therefore they dont create communication systems' load. (For example, unsuccessful calls, waiting for the next attempt, are in "the head of" the user only. The calls and devices in the environment form the intent and repeated calls flows). Calls leave the environment (and the model) in the instance they enter a Terminator virtual device;

A-7. (Parameters' undependability) We consider probabilities for direction of calls to, and holding times in the base virtual devices as independent of each other and from intensity Fa = inc.Fa of incoming flow of calls. Values Networks and Telecommunications of these parameters are determined by users' behavior and technical characteristics of the communication system. (Obviously, this is not applicable to the devices of type Enter Switch, correspondingly to Pbs and Pbr);

A-8. (Randomness) All variables in the analytical model may be random and we are working with their mean values, following the Theorem of Little.

A-9. (B-Terminal Occupation) Probabilities of direction of calls to, and duration of occupation of devices ar, cr, ac and cc are the same for A and B-calls;

A-10. (Channel Switching) Every call occupies simultaneously places in all the base virtual devices in the telecommunication system (comprised of devices a or b) it passed through, including the base device where it is in the moment of observation. Every call releases all its occupied places in all base virtual devices of the communication system, in the instant it leaves comprising devices a or b.

A-11. (Terminals' Homogeneity) All terminals are homogeneous, e.g. all relevant characteristics are equal for every terminal;

A-12. (A-Calls Directions) Every A-terminal directs uniformly all its calls only to the other terminals, not to itself;

A-13. (B-flow ordinariness) The flow directed to B-terminals (Fb) is ordinary. (The importance of A-13 is limited only to the case when two or more calls may reach simultaneously a free B-terminal. A-13 may be acquitted from results like in (Burk 1956) and (Vere-Jones 1968);

A-14. (B-Blocking Probability for Repeated attempts) The mean probability (Pbr) of a call to find the same B-terminal busy at the first and at the all following repeated attempts is one and the same.

3. Analytical Model 3.1. Some General Equations For the proposed conceptual model we derived the following system of equations (Poryazov, Saranova 2005):

Yab = Fa[S1 - S2(1 - Pbs) Pbr - S3 Pbs] (1.1) Fa = dem.Fa + rep.Fa (1.2) dem.Fa = Fo (Nab + M Yab) (1.3) rep.Fa = Fa [R1 - R2 Pbr (1 - Pbs) - R3 Pbs] (1.4) Yab- in case of 1 Yab Nab, Pbr = Nab- (1.5) 0 in case of 0 Yab < 1.

Ts = S1Z - S2Z Pbr (1.6) ofr.Fs = Fa (1- Pad )(1- Pid ) (1.7) ofr.Ys = ofr.Fs Ts (1.8) Pbs = Erl_b ( Ns, ofr.Ys) (1.9) crr.Ys = (1- Pbs) ofr.Ys (1.10) Fourth International Conference I.TECH 2006 The following notations are used:

S1 = Ted + Pad Tad + (1 - Pad )[Pid Tid + (1 - Pid )[Tcd + PisTis + (2.1) (1- Pis)[PnsTns + (1- Pns)[Tcs + 2Tb]]]] S2 = (1 - Pad )(1 - Pid )(1 - Pis)(1 - Pns)[2Tb - Tbr] (2.2) S3 = (1 - Pad )(1 - Pid )[PisTis + (1- Pis)[PnsTns + (2.3) (1 - Pns)[Tcs + 2Tb]]] -(1- Pad )(1- Pid)Tbs S1z = PisTis + (1 - Pis)[PnsTns + (1 - Pns)(Tb + Tcs)] (2.4) S2z = (1 - Pis)(1 - Pns)(Tb + Tcs) (2.5) R1 = Pad Prad + (1 - Pad ) (Pid Prid + (1 - Pid ) Pis Pris + (2.6) (1 - Pis)(Pns Prns + (1 - Pns ) Q) R2 = (1- Pad)(1- Pid)(1- Pis)(1- Pns)(Prbr - Q) (2.7) (2.8) R3 = (1- Pad)(1- Pid){PisPris + (1- Pis)[PnsPrms + (1- Pns)Q] - Prbs} (2.9) Q = Par Prar + (1- Par)[Pac Prac + (1 - Pac) Prcc] An important assumption for proposed analytical model is:

The intent intensity of calls of one idle terminal is Fo 0.

3.2. General Blocking Probability Based on the conceptual model we define general blocking probability as follows:

Definition: General blocking probability (Pbl):

Pbl = {Pbr Pbs, Pbr (0,1), Pbs (0,1) :

(1- Pad )(1- Pid) Pbs + (1- Pbs)(1- Pis)(1- Pns) Pbr} (2.10) Pad, Pid, Pis, Pbs, Pns, Pbr, Par, Pac and Pcc are known probabilities (see the conceptual model).

3.3. Probabilities of Blocking Switching (Pbs) and of Finding B-Terminal Busy (Pbr).

If Pbr [0,1], Pbs (0,1] then each duple (Pbr, Pbs) define a value of Pbl throw (2.10) and back, each value of Pbl define a set of duples (Pbr, Pbs).

As GoS- parameter we consider general blocking probability Pbl based on (2.10).

Analogously, adm.Pbl (administratively determined value of Pbl in SLA in advance) defines set of duples (adm.Pbr, adm.Pbs) and back.

We consider general blocking probability (adm.Pbl) as a main QoS parameter, administratively determined in advance in SLA.

Networks and Telecommunications 4. Network Dimensioning Task 4.1. Formulation of a Network Dimensioning Task (NDT):

1. To be dimensioned a network (to be found necessary number of internal switching lines), when in advance level of QoS is administratively determined and the values of known parameters are dimensioned and/ or calculated.

2. To be found the values of the unknown parameters, describing the system state in the upper case. For example, a system parameter, describing macrostate of the system (through the value of Yab), a terminal capacity of the system (the maximal number of active terminals Nab), intensity of demanded and repeated call attempts (respectively dem.Fa and rep.Fa), offered to the switching system traffic intensity (ofr.Ys) and others.

Parameters in the Network Dimensioning Task:

Administrative determined parameters:

adm.Pbl and M (3.1) Known parameters:

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