Yieh-Ran Haung IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY JANUARY 2003 李孝治

1. Determining the Optimal Buffer Size for Short Message Transfer in a HeterogeneousGPRS/UMTS Network Yieh-Ran Haung IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY JANUARY 2003 李孝治

2. Abstract • Multimedia messaging service (MMS) enables the transmission of messages with full content versatility between mobile devices and from applications to these devices, which can be used over the general packet radio service (GPRS) / universal mobile telecommunications system (UMTS) short message service (SMS) network.

3. In the GPRS/UMTS SMS network, the serving GPRS support node (SGSN) shall store the mobile-terminated message in a queue until it is successfully transferred to the mobile device or its maximum waiting time expires. • The queued message is forwarded to the new SGSN and is immediately removed from the waiting queue of the old SGSN, if the corresponding mobile device leaves the old SGSN area before the waiting time expires.

4. Taking the forwarding and the expiration effects of queued messages into account, this paper develops an analytical model to study the system performance of a heterogeneous GPRS/UMTS SMS network, in which the parameters (e.g., message arrival rate, SGSN area residence time, buffer size, etc.) of SGSNs can be varied.

5. On the basis of the analytical model, an iterative method is proposed to determine the optimal buffer size so that the available bandwidth is fully utilized and the message loss probability is minimized.

6. I. INTRODUCTION • SMS (Short Message Service) • Launched in 1992 • For GSM (Global System for Mobile communications) • The most successful wireless data service • Text-based messages • Up to 160 characters • EMS (Enhanced Message Service) • Combination of text, simple pixel-images, and melodies

7. MMS (Multimedia Message Service) • Full content versatility, including text, images, audio, and video • The standard is still evolving, and new functions and features will continue to be added. • MMS is designed to exploit the potential of high-bandwidth wireless networks, such as General Packet Radio Service (GPRS) and Universal Mobile Telecommunications System (UMTS) [2]. • MMS can be used over the GPRS/UMTS SMS network.

8.        • MS = GPRS Mobile Station • UE = UMTS User Equipment • SGSN = Serving GPRS Support Node • SMS-IWMSC = Short Message Service Interworking Mobile Switching Office • SM-SC = Short Message Service Center • SMS-GMSC = Short Message Service Gateway Mobile Switching Office • HLR = Home Location Register

9. SGSN Buffing • The SGSN shall store the mobile-terminated message in a queue until it is successfully transferred to the MS/UE or its maximum waiting timeexpires. • The queued message is forwarded to the new SGSN and is immediately removed from the waiting queue of the old SGSN, if the corresponding MS/UEleaves the service area of the old SGSN (i.e., the MS/UE initiates an inter-SGSN routing area update [2]) before the waiting time expires.

10. ProblemofSGSN Buffing • Once the SGSN’s buffer is full, all incoming mobile-terminated messages must be discarded and retransmitted from the SM-SC later. • The messages, especially the forwarded messages, suffer from a longerdelay before being successfully delivered. • If the buffer is not big enough, the available bandwidthcannot be fully utilized and the system will experience larger message loss probability. • A too big buffer would lead to poorresource utilization.

11. The goal • This paper develops an analytical model to study the system performance of a heterogeneousGPRS/UMTS SMS network, in which the parameters (e.g., message arrival rate, message transmission time, SGSN area residence time, buffer size, etc.) of SGSNs can be varied.

12. On the basis of the analytical model, an iterative method is proposed to determine the optimalbuffer size so that the available bandwidth is fully utilized and the message loss probability is minimized. • Besides, the effects of changing the important parameters, including the call-to-mobility ratio (CMR) and the message expiration rate, on the system performance and the optimal buffer size are studied.

13. II. GPRS/UMTS SHORT MESSAGE TRANSFER • AL = Application Layer • TL = Transport Layer • RL = Relay Layer

14. Transport Layer • SMS-SUBMIT • Transferring a short message from the MS/UE to the SM-SC • SMS-DELIVER • Transferring a short message from the SM-SC to the MS/UE • SMS-COMMAND • Invoking an operation at the SM-SC, e.g., delete a message, enquire the status of a previously submitted message, etc. • SMS-STATUS-REPORT • Informing the MS/UE of the status of a previously submitted message.

15. Relay Layer • RP-MO-DATA • Transferring a mobile-originated TPDU • RP-MT-DATA • Transferring a mobile-terminated TPDU • RP-ACK • confirming the receipt of a relay protocol data unit (RPDU) • RP-ERROR • Informing of an unsuccessful RPDU transfer attempt

16. A. Mobile-Originated short message transfer procedures.

17. B. Mobile-Terminated short message transfer procedures.

18. III. SYSTEM MODEL • M SGSNs • Routing probability rij • From the service area of SGSN i to the service area of SGSN j • Each SGSN k is modeled by a continuous-time model with the following parameters and assumptions: • The newlyarriving mobile-terminated messages are Poisson distributed with a rate of λnk.

19. A queued message is forwarded to the new SGSN and is immediately removed from the waiting queue of the old SGSN, if the corresponding portable leaves the service area of the old SGSN before the timeout period expires. It is assumed that the forwarded messages are generated according to a Poisson distribution with a rate of λfk. • A queued message is immediately removed from the waiting queue unless it can be successfully transmitted within its timeout period. The timeout period of the queued messages is assumed to be exponentially distributed with a mean of 1/γk.

20. The queued messages are transmitted in a first-in first-out (FIFO) manner, in order to guarantee message sequence integrity*. The transmission time of a message is assumed to be exponentially distributed with a mean of 1/μk. • The size of the service area of an SGSN is indirectly reflected by the SGSN area residence time. If the size of the SGSN area is small, the mean SGSN area residence time will be relatively small, and vice versa. The SGSN area residence time of a portable is assumed to be exponentially distributed with a mean of 1/ηk. • The buffer has capacity for Bk messages . eta

21. IV. ANALYSIS • One-dimensional Markov chain with state si where i denotes the number of messages in buffer. • Let pibe the steady-state probability for si. Using the Markovchainbalance equations, the steady-state probability is given by (1) where

22. Parameters used in the system model SGSNk-1 Entering λfk New Arrival Transmitted λnk μk MS/UE SGSNk MS/UE Removed Leaving ηk γk SGSNk+1 Note: Call-mobility Ratio CMR = λn/ η

23. A. Waiting Time • The waiting time of a message (newly arriving or forwarded) in SGSN is defined as the time between the acceptance of such a message by the SGSN and its being transmitted, which can be derived as follows. • Under the condition that the message is transmitted, the average waiting time of the message can be expressed as where Prob{transmit|si} is given in (7), and E[Ti and transmit|si} can be calculated from (5) and (6) as follows:

27. Under the condition that the message is transmitted, the average waiting time of the message can be expressed as where Prob{transmit|si} is given in (7), and E[Ti and transmit|si} can be calculated from (5) and (6) as follows:

29. B. LossProbability • A message may be discarded for one of two reasons. • The buffer is full when a message arrives. • A message, although accepted and waiting in the queue, fails to be transmitted within its timeout period. • The message loss probability in SGSN k, Lk, can thus be expressed as where Prob{expire|si} is given in (5).

30. C. Optimal Buffer Size • B*k • The smallest size that achieves maximumbandwidth utilization and minimummessage loss probability. • Directly affected by the forwarded message arrival rate λfk. • An iterative method, as shown in Fig. 6, to determine λfk and B*k.

31. Fig. 6. Iterative method for determining λfk and B*k.

32. The rate of the queued messages moving out of SGSN is given by where Prob{forward|si} is given in (6). • The rate of forwarded messages moving into SGSN , can be expressed as

33. Routing matrix V. NUMERICAL RESULTS • Simulation model • An event-driven simulation • A two-dimensional GPRS/UMTS SMS network

34. Significant difference Buffer size   Loss Probability  Fig. 8 Comparison of simulation and analytical results (λ /η = 1).

35. Significant difference Buffer size   Waiting time  Fig. 8 Comparison of simulation and analytical results (λ /η = 1).

36. Insignificant difference (low mobility) Buffer size   Loss Probability  Fig. 9. Comparison of simulation and analytical results (λ /η = 100).

37. Insignificant difference (low mobility) Buffer size   Waiting time  Fig. 9. Comparison of simulation and analytical results (λ /η = 100).

38. λ / η  Loss probability  Fig. 10. Performance measures of the hot SGSN versus buffer size for different λ /η.

39. λ / η  Waiting time  Fig. 10. Performance measures of the hot SGSN versus buffer size for different λ /η.

40. γ  Loss probability γ  Loss probability Fig. 11. Performance measures of the hot SGSN versus buffer size for differentγ.

41. γ  Waiting time  Fig. 11. Performance measures of the hot SGSN versus buffer size for differentγ.

42. VI. CONCLUSION • The numerical results yielded the following observations. • CMR  Message waiting time Message loss probability  Optimal buffer size • Message expiration rate Message waiting time Message loss probability  (under smaller buffer size) Message loss probability  (under larger buffer size) Optimal buffer size End