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Prof. Oleg Zaikin

Queuing based approach to TDM-channels assignment. in the global maritime system Inmarsat-C. Prof. Oleg Zaikin. Technical University of Szczecin Depatrment of Computer Network and Information Community. Zolnierska 49, 71-210, Szczecin, Poland tel. (+4891) 449-56-63

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Prof. Oleg Zaikin

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  1. Queuing based approach to TDM-channels assignment in the global maritime system Inmarsat-C Prof. Oleg Zaikin Technical University of Szczecin Depatrment of Computer Network and Information Community Zolnierska 49, 71-210, Szczecin, Poland tel. (+4891) 449-56-63 e-mail: ozaikine@wi.ps.pl

  2. OBJECTIVE The development of the stochastic approach, based on queuing modelling and simulation To solve the problem of the resource assignment In the distributed networks APPLICATION AREAS • Proposed approach is oriented towards: • Electronic Industry, • Telecommunication, • Computer networks • Multimedia environment.

  3. TASKS OF QUEUING NETWORK OPTIMIZATION • PARAMETERS OF QUEUING NETWORK • Network topology • Resources allocation • Traffic flow management • TASKS OF QUEUING NETWORK OPTIMIZATION • Optimisation of configuration of QN • Optimisation of the resources allocation • Optimisation of the traffic routing

  4. Network configuration (on example of STS Inmarsat-C) NCC NCS NCS LES LES LES LES Public terrestrial network MES MES MES MES

  5. TDM CHANNEL DISTRIBUTION There are three possible kinds of TDM channels allocation among LES: 1. Fixed Distribution Sig Ch TDM Ch Sig Ch 11 12 13 21 22 23 .............................. k1 k2 k3

  6. TDM CHANNEL DISTRIBUTION There are three possible kinds of TDM channels allocation among LES: 2. Dynamic Distribution Sig Ch TDM Ch Sig Ch 11 12 13 NCS NCS 21 22 23 ... .................. k1 k2 k3

  7. TDM CHANNEL DISTRIBUTION There are three possible kinds of TDM channels allocation among LES: 3. Mixed Distribution Sig Ch TDM Ch Sig Ch 11 12 13 21 22 23 31 32 33 NCS NCS 41 42 43 .... .................. k1 k2 k3

  8. Channel usage NSL TxN DaN NCC NCS ISL SC SC DTE LES MES (DCE) MC TDM EGC

  9. Variable TDM assignment MES NCS LES TN tr Request ta1 DAMA ta2 Assignment Assignment Message (0) Message (1) tmsg Message (n) tconf Confirmation td Delivery Clearing tcl Clearing

  10. Problem Statement • For given: • Set of terrestrial regions (global and local) R={rk}, k=1,K, • set of land stations S={sk}, k=1,K and • land station parameters (sk)=(ek,Gk), • Set of telecommunication streams F={fi}, i=1,I, • telecommunications stream routes , i=1,I and • parameters (fi)={i(n,t),i}, • Total number of TDM channels, assigned for global region HT, and channels parameters • (cF, cD)=({F,F},{D,D}), where {F, D} and {F, D} – performance and cost of fixed • and dynamic channels correspondingly, F<D, F>D • It is demanded to define a number of TDM channels, having to manage by the NCS Hc, • And a number of TDM channels, assigned for each land station skS, Hk, k=1,K, providing minimum of average • Processing time of the incoming calls at STN • with the following restrictions • The total number of TDM channels at global region R • Minimal admissible value of channels utilization • where - utilization of fixed and dynamic channels correspondingly

  11. Control parameters The assignment of channels can be described by the matrix where Criterion of task The processing time for one call where tc – the communication time ts – servicing time The total processing time for all calls in all regions in a given period T0 is defined by formula where si,sj – LES indexes, T0 – the period of optimisation From the feature of additivity we get where TC – the total time spent communication TS – the total time spent servicing for all calls.

  12. Criteria For one call the total time of service , where is the total time of waiting for one call and is The total time of processing of one call. The first component can be calculated from the formula where - p is probability of TDM channel being busy during the call (no free slots avaible) - is the average time of waiting before the next attempt to call (retry time). The component can be calculated from the formula where - is duration of the request on the signalling channel, - is the time needed to assign TDM channel (incl. Frequency and time slot), - is the duration of message itself. This value depends on the length of message and the number of slots per frame assigned for the transmition, - is the time of delivering the message to the client of the terrestrial network, - is the duration of clearing of the call. Restriction There may exist several TDM channels occupying the same frequency as long as they are transmitted in non-overlapping spot beams.

  13. Criteria of optimisation Total processing time of all the incoming calls, at all the land stations, during period of optimizationT0, where k=1,K – index of land stations sk, i=1,I – index of telecommunication stream fi, i – rate of arrival patterns of stream fi, ti – average processing time of a call pifi, Q(s1)(fi) – Kronecker symbol, The value ti can be expressed, as the sum of two components where - communication time of call - servicing time of call

  14. Criterion function analysis As it is shown from expressions for objective function only the second component of criterion function depends on control parameters values. Therefore, total servicing time depends on control parameters Hc, Hk, k=1,K. The given criterion function is additive relatively each land station skS. Therefore, to define the value of criterion function it is enough to define total servicing time for each LES skS Let us show, that each LES represents a multi-channel queuing system.

  15. ... IB OB P 3,k P 2,k P 1,k ... ... Structure of queuing system with different kinds of several and limited capacities of input (IB) and output (OB) queues

  16. Solution method • QUEUING SYSTEM THEORY: analytical solution for primary evaluation • SIMULATION APPROACH: simulation model design Analytical method (STRUCTURE OF QUEUING SYSTEM IS THE SAME AS THE SLIDE BEFORE) Hk,k=1,K – a number of TDM channels, assigned for land station, Pk1 – probability of that a number of calls incoming at a moment at LES sk is less than a number of private serversHk, - service time of a call with private servers, Hc – a number of TDM channels, having to manage by the NCS (centralized channels), Pk2 – probability of that a number of calls incoming at a moment at LES sk is more than a number of private servers Hk, but less than maximal number of leased servers HD, - service time of a call with leased servers, Pk3 – probability of that a number of calls incoming at a moment at LES sk is more than total number of servers Hk+HD (all the channels are occupied).

  17. Analytical method (cont.) It’s obvious, that Pk1+Pk2+Pk3=1, - repeating time for a call. For Poisson process probability of that for time t a number of incoming calls is no more than n is determined by integrated distribution function where  - rate of stream, n – maximal number of calls served by QS (a number of servers) s – average service time of a call,

  18. Analytical method (cont.) Therefore, if k – servicing time of one call at LES Sk, then Here Probability P can be defined with Laplace integral with the formula

  19. Simulation model The aim of simulation is to define optimal configuration of STS. It means, that time of servicing of allthe communication demands will be minimal. To compose the simulation model the program MATLABwill be applied, which is the integrated environment for statistics and numeric methods, matrix operationswith simple and efficient programming language. Additional advantage of MATLAB is advanced tools of two and three-dimensional graphics for data visualization. Such simulation model has not any restrictions for dimension, kind of arrival pattern, discipline and time ofservicing queuing systems. To design the simulator the program MATLAB will be applied, which is the integrated environment for statisticsand numeric methods, matrix operations with simple and efficient programming language. A tool for manufacturing systems analysis, this simulation program can be used at various areas, for example incomputer networks, manufacturing flexible systems and telecommunication.

  20. Example of realization It is given the following task Satellite telecommunication network, servicing an ocean region, consists of one NCS and five LES. Each of themprovides communication demands of some terrestrial region and these demands can considerably differ (traffic stream and expectation). There is the prossibility of centralized, decentralized and mixed organization of resources allocation for all globalregions. There are 30 TDM channels for global region overall. Each of them includes time frames with 23 time slots, operatingcommunication calls in parallel. It is necessary to allocate all the TDM channels between NCS and all the LES in order to minimize total servicing time for all communication calls at all areas of ocean region during period of optimization T0.

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