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We have embedded the model to the multiframe end instants. Hence, we have modified the approach proposed in [10], by taking into account that packets have a compound arrival process due to both the generation process of datagrams and their variable length in packets. Hence, the packet arrival process is characterised by the following probability-generating matrix:
where: ??? ?a is the mean datagram arrival rate during an activity period
??? L(z) is the probability-generating function for the length of a datagram in packets (in this case the compressed deck length is considered)
??? TMFis the multiframe duration ??? p12 = TMF?a/Nd is the probability that the source leaves the activity phase in TMF ??? p11 = 1 - p12 ??? p21 = TMF?id is the probability that the source leaves the idle phase in TMF ??? p22 = 1 - p21
According to (3) and [10], we obtain the following expression for Tdtg
?
???????????
?
where ??= ?TMFMwLd erlangs (Ld being the mean length of a datagram in packets) is the traffic intensity produced by Mw users and parameters ?1’’(1) and ??w’(1) have complex expressions that can
be found in [10]. For stability reasons the traffic load ??must be lower than 1.
5. Results
This Section presents the obtained results on the basis of both the traffic model and the analyticalapproach outlined in the previous Sections. Fig. 4 shows the behaviour of the mean datagram delay,Tdtg, as a function of the number of mobile terminals that simultaneously make browsing with WAPper SDCCH channel, Mw. These results have been obtained through w
formula (4) and by using thestatistical characteristics of the length of a datagram in packets according to Section III with Nc = 3 or4 cards/deck (correspondingly, the mean number of packets per datagram, i.e., a deck, is equal to 4.3 ,5.5 and the mean squared value is equal to 29.4 , 50.8). This graph shows three cases for the meannumber of datagrams per activity period, i.e., Nd = 2, 3 and 4. The mean datagram delay increases withMw. Of course, the greater Nd and/or Nc the greater the mean datagram delay (e.g., in the case Nd = 4,we have Tdtg close to 4 s for both Mw = 5 with Nc = 4 cards/deck and Mw = 8 with Nc = 3 cards/deck).It is worth noting that Tdtg represents the datagram delay due to the available capacity. An additional delay is also present due to the connection set-up for the transmission of each SMS in which the datagram is segmented. In the considered network configuration with local SMSC, we can roughlyestimate that the connection set-up time for each SMS is about equal to two multiframes (onemultiframe for the request and another for the response) and that 1 SMS is on average required percard. Anyway, a graph like that presented in Fig. 4 may be useful to show the QoS levels attainablewith WAP over GSM-SMS. According to these results, it is possible to design the tourist serviceenvisaged in this study as follows: (i) for the GSM operator: dimensioning of the number of GSMsignalling channels to provide a service with an adequate QoS level (i.e., Tdtg lower than a specifiedvalue, for instance 4 s); (ii) for the service provider: defining the number of cards per deck so that each
user can receive the deck without annoying delays. The results shown in Fig. 4 highlight the limits ofthe GSM-SMS service as a support for WAP. A further study is required to consider the case wherethe General Packet Radio Service (GPRS) and the related packet switched network elements (GSM phase 2+) are used to convey WAP datagrams.
This paper has presented a preliminary study on the QoS evaluation for mobile browsing through
WAP over GSM-SMS. A tourist service at the city level has been envisaged. Accordingly, a suitable
network architecture has been proposed. A model has been defined to characterise the downlink traffic
produced by browsing users with WAP. The length in bytes of the cards within decks has been
statistically characterised by considering many examples found in different WAP servers. An
analytical approach has been described that allows predicting the mean deck delay as a function of the
number of users simultaneously involved in WAP sessions. This result permits to estimate the QoS
provided to users so that useful considerations can be obtained for designing WAP services.
References
[1] S. Nanda, K. Balachandran, S. Kumar, “Adaptation Techniques in Wireless Packet Data
services”, IEEE Communications Magazine, pp. 54-64, January 2000. [2] http://www.wapforum.org/what/WAP_white_pages.pdf
[3] S. M. Redl, M. K. Weber, M. W. Oliphant. An Introduction to GSM. Artech House, MA, 1995
[4] ETSI, “Digital Cellular Telecommunications System (Phase 2+); Point-to-Point (PP) short
Message Service (SMS) Support on Mobile Radio Interface” (GSM 04.11). [5] Wireless Application Protocol Forum Ltd, WAP-158, Wireless Datagram Protocol
Specification, Version November 5, 1999.
[6] ETSI - Digital cellular telecommunications system (Phase 2+); Technical realization of the
Short Message Service (SMS); Point-to-Point (PP) (GSM 03.40).
[7] Wireless Application Protocol Forum, Ltd, WAP-154, Binary XML Content Format
Specification, Version 1.2, 4 November 1999.
[8] ETSI - Digital cellular telecommunications system (Phase 2+); Channel coding, (GSM 05.03
version 5.5.0)
[9] A. E. Brand, A. H. Aghvami, “Multidimensional PRMA with Prioritized Bayesian Broadcast – A MAC Strategy for Multiservice Traffic over UMTS”, IEEE Trans. Veh. Tech., Vol. 47, No. 4, pp. 1148-1161, November 1998.
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