- Email: [email protected]
UMTS networks
Information Sciences 170 (2005) 235–249 www.elsevier.com/locate/ins
Overload control for short message transfer in GPRS/UMTS networks q Yieh-Ran Haung a
a,*
, Jan-Ming Ho
b
Department of Computer Science and Engineering, Yuan Ze University, 135 Yuan-Tung Rd., Chung-Li, Toayuan 320, Taiwan b Institute of Information Science, Academia Sinica, Taipei 115, Taiwan Received 12 June 2003; accepted 20 February 2004
Abstract In the General Packet Radio Service (GPRS)/Universal Mobile Telecommunications System (UMTS) short message service (SMS) network, the serving GPRS support node (SGSN) stores the 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 valid queueing time expires. Once the SGSN’s buffer is full, all incoming messages must be discarded and retransmitted later. Under this situation, the messages, especially the forwarded messages, suffer from a longer delay before being successfully delivered. To prevent messages from being excessively delayed, this paper proposes an SGSN overload control scheme called the N -overload scheme. According to this scheme, a newly arriving message is discarded if the buffer is full upon its arrival. A forwarded message, however, is queued in an overload space of size N. Taking the forwarding and the expiration effects of queued messages into account, this paper also develops an analytical model to study the performance for the SGSN using the N -overload scheme. On the basis of the analysis, the optimal value of N is numerically determined so that the loss probability for the forwarded messages is minimized. 2004 Elsevier Inc. All rights reserved.
q
This work was supported by NSC under contract 92–2213–E–155–035. Corresponding author. Fax: +886-34638850. E-mail addresses: [email protected] (Y.-R. Haung), [email protected] (J.-M. Ho). *
0020-0255/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2004.02.023
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Keywords: GPRS; UMTS; SMS; SGSN; Overload control
1. Introduction Global System for Mobile communications (GSM) short message service (SMS) has become the most successful wireless data service. GSM SMS allows mobile users to send and receive text-based messages of up to 160 characters. The recently introduced enhanced messaging service (EMS), which offers a combination of text, simple pixel-images, and melodies, can be seen as an extension of GSM SMS with each of its messages being handled as a series of concatenated SMS messages. This means that operators can continue to use and derive income from current GSM networks. However, it is crucial that operators ensure their infrastructure have the necessary capacity to handle the increase in message traffic, especially when multimedia messaging service (MMS) [1] arrives and takes off. MMS is a new global messaging standard that enables the transmission of messages with full content versatility, including text, images, audio, and video, between mobile devices and from applications to these devices. MMS can be used over the General Packet Radio Service (GPRS)/Universal Mobile Telecommunications System (UMTS) SMS network [2,3]. The GPRS/UMTS SMS network architecture is illustrated in Fig. 1. In this architecture, when a GPRS mobile station (MS) or a UMTS user equipment (UE) sends a short message, this message is delivered to an SMS interworking mobile switching center (SMS-IWMSC) via the serving GPRS support node (SGSN). The SMS-IWMSC passes this message to an SMS center (SM-SC). The SM-SC forwards the message to an SMS gateway MSC (SMS-GMSC). Upon receipt of the message, the SMS-GMSC interrogates the home location register (HLR) for routing information and sends the message to the appro-
Originating MS/UE SMSIWMSC
SGSN
HLR
SM-SC
Terminating MS/UE SGSN
SMSGMSC
Fig. 1. GPRS/UMTS SMS network architecture. (For color see online version.)
Y.-R. Haung, J.-M. Ho / Information Sciences 170 (2005) 235–249
MS/UE
SGSN
IWMSC
237
SM-SC
(1) Send RPDU (1) Forward RPDU (1) Forward RPDU (2) Send RPAU (2) Forward RPAU (3) Send RPSU
(2) Forward RPAU (3) Forward RPSU (3) Forward RPSU
Fig. 2. Mobile-originated short message transfer procedure.
priate SGSN. The SGSN then delivers the message to the terminating MS/UE. In the following, we elaborate on the mobile-originated and the mobile-terminated short message transfer procedures. 1.1. Mobile-originated The message flow of the mobile-originated short message transfer procedure is shown in Fig. 2, and is explained in the following steps. (1) The MS/UE forms a relay protocol data unit (RPDU) containing the short message submitted, the addresses of the terminating SM-SC and MS/UE, the Validity-Period indicating the time period for which the message is valid, and the Status-Report indicating if the originating MS/UE requests a delivery report. Then, the MS/UE sends the RPDU to the IWMSC through the SGSN. After receiving the RPDU, the IWMSC establishes a link with the addressed SM-SC and forwards the RPDU to the SM-SC. (2) Upon receipt of the RPDU, the SM-SC sends a relay protocol acknowledgement unit (RPAU) to the MS/UE via the IWMSC and the SGSN for confirming that the SM-SC has received the submitted short message. (3) If the Status-Report described in Step (1) indicates that the originating MS/ UE requests a delivery report, the SM-SC shall send a relay protocol status unit (RPSU) with the status of the submitted short message (e.g., successfully delivered or dropped) to the MS/UE. 1.2. Mobile-terminated Fig. 3 depicts the message flow of the mobile-terminated short message transfer procedure. Each step is explained as follows.
238
Y.-R. Haung, J.-M. Ho / Information Sciences 170 (2005) 235–249 GMSC
SM-SC
HLR
old SGSN
new SGSN
MS/UE
(1) Send RPDU (2) MAP-SENDROUTINGINFO-SM (2) MAP-SENDROUTINGINFO-SM-ACK (2) Forward RPDU (3) Forward RPDU (3) Forward RPDU
(5) Forward RPAU/RPEU
(5) Forward RPAU/RPEU
(4) Send RPAU/RPEU
(5) Forward RPAU/RPEU
Fig. 3. Mobile-terminated short message transfer procedure.
(1) The SM-SC forms an RPDU containing the short message to be delivered and the address of the terminating MS/UE, and then sends the RPDU to the GMSC. (2) When receiving the RPDU, the GMSC sends a MAP-SEND-ROUTINGINFO-SM message [4] to the HLR. If the HLR determines that the short message transfer request can be served, it returns a MAP-SEND-ROUTING-INFO-SM-ACK message with the SGSN address to the GMSC. The GMSC then forwards the RPDU to the SGSN indicated by the HLR. (3) The SGSN transfers the RPDU to the terminating MS/UE. Notice that the SGSN shall store the RPDU in a queue until it is successfully transferred to the MS/UE or its maximum queueing time expires. The maximum queueing time must be shorter than the Validity-Period described in Step (1) of Fig. 2. A queued message is forwarded to the new SGSN and is immediately removed from the waiting queue of the old SGSN, if the corresponding MS/UE leaves the service area of the old SGSN (i.e., the MS/UE initiates an inter-SGSN routing area update [5]) before the valid queueing time expires. If the forwarded message is discarded due to buffer overflow or is not successfully transferred to the MS/UE within the permitted time, the new SGSN returns an appropriate error to the SMS-GMSC through the old SGSN. (4) If the short message delivery was successful, the MS/UE sends an RPAU to the new SGSN. Otherwise, a relay protocol error unit (RPEU) with an appropriate cause is sent to the new SGSN. (5) If the RPAU was received within the valid time period, the new SGSN forwards the RPAU to the SM-SC via the old SGSN and the GMSC. Other-
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239
wise (i.e., the stored RPDU can not be successfully delivered to the MS/UE within the permitted time), the new SGSN removes the RPDU from the queue and returns an RPEU with an appropriate cause to the SM-SC. As mentioned above, the SGSN shall store the mobile-terminated message in a queue until it is successfully transferred to the MS/UE 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 MS/UE leaves the service area of the old SGSN before the valid queueing time expires. Once the SGSNs buffer is full, all incoming mobileterminated messages must be discarded and retransmitted from the SM-SC later. Under this situation, the messages, especially the forwarded messages, suffer from a longer delay before being successfully delivered. The purpose of overload control for short message transfer in an SGSN is therefore to protect forwarded messages against newly arriving ones so as to prevent forwarded messages from being excessively delayed, which is especially needed for multimedia messages. This paper proposes an SGSN overload control scheme called the N -overload scheme. According to this scheme, a newly arriving message is discarded if the buffer is full upon its arrival. A forwarded message, however, is queued in an overload space of size N . Taking the forwarding and the expiration effects of queued messages into account, this paper also develops an analytical model to study the performance for the SGSN using the N -overload scheme. On the basis of the analysis, the optimal (smallest) value of N is numerically determined so that the loss probability for the forwarded messages is minimized. The effects of changing mobility and expiration parameters on the optimal value of N are also studied. The paper is organized as follows. Section 2 presents the analytical model for the SGSN using the N -overload scheme. Section 3 shows some numerical results to investigate the optimal value of N under various mobility and expiration parameters, and to study the effects of changing these parameters on the optimal value of N . Finally, Section 4 concludes the paper.
2. The analytical model Each SGSN in a GPRS/UMTS SMS network is modelled by a continuoustime model with the following parameters and assumptions. • The buffer has capacity for B messages. • The overload space has capacity for N messages. • The newly arriving mobile-terminated messages are Poisson distributed with a rate of kn . A newly arriving message is discarded if the buffer occupancy is
240
• •
•
•
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B, while a forwarded message is discarded only when the overload-space occupancy is N . The transmission time of a message is exponentially distributed with a mean of l1. 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 exponentially distributed with a mean of 1c, as in [6–9]. 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. The forwarded messages are accepted as long as the buffer is not full, and are generated according to a Poisson distribution with a rate of kf . Notice that kf is correlated with other parameters (e.g., portable mobility, message transmission time, timeout period, etc.) and can be determined by an iterative method (see Section 2.1). The SGSN area residence time of a portable is exponentially distributed with a mean of 1g. Although the residence times are typically non-exponential in a particular mobile system, the analysis based on the simplified exponential assumption has been widely used [10–13] and does provide useful mean value information for the output measures.
The above queueing model can be described by a one-dimensional Markov chain with states si where i denotes the number of messages in buffer. Fig. 4 describes the state diagram. Let pi be the steady state probability for si . Using the Markov chain balance equations, the steady state probability is given by 8Q n f < ij¼1 k þk p0 ; if 1 6 i 6 B; xj f ð1Þ p i ¼ QB n f Qi k þk k : ; if B þ 1 6 i 6 B þ N ; p 0 j¼1 j¼Bþ1 xj xj PBþN where xj ¼ l þ jðg þ cÞ and i¼0 pi ¼ 1. In the following, general expressions will be derived to calculate the forwarded message arrival rate, the message loss probability, and the message waiting time in the SGSN. 2.1. Forwarded message arrival rate This section proposes an iterative method to determine the forwarded message arrival rate kf . Suppose that a message mi arrives at time t when the
Fig. 4. State diagram.
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241
SGSN is in state si . Consider the i outstanding messages that arrive at the SGSN earlier than mi . Among these i messages, the first leaves the SGSN (either the message is transmitted, expires, or is forwarded to a new SGSN) at time t þ ti ; the second leaves the SGSN at time t þ ti þ ti1 , and the ith message leaves the SGSN at time t þ ti þ ti1 þ þ t1 . Under the memoryless conditions, the probability density function for ti is given by f ðti Þ ¼ ½l þ iðg þ cÞe½lþiðgþcÞti :
ð2Þ
Let Ti denote the time elapsed before the message mi is transmitted (i.e., Ti ¼ t1 þ t2 þ þ ti ). Also, let s be the timeout period for mi , and x be the period between the arrival of mi and the time when the corresponding portable leaves the service area of the SGSN. The probability density functions of s and x can be expressed as fs ðsÞ ¼ cecs
ð3Þ
fx ðxÞ ¼ gegx ;
ð4Þ
and
respectively. As mentioned earlier, a queued message (within its timeout period) is forwarded to the new SGSN if the corresponding portable leaves the service area of the old SGSN before being transmitted. That is, the message mi is forwarded to a new SGSN if x < s and x < Ti . Thus, the probability that the message mi is forwarded to a new SGSN can be expressed as Probfforward j si g ¼ Probfx < s and x < Ti j si g Z 1Z s fx ðxÞfs ðsÞ dx ds ¼ s¼0
Z
x¼0 1
Z
ti ¼0
¼
Z
1
Z
t1 ¼0
Z
s¼0
¼
Z
Ti ¼t1 þþti
fx ðxÞ
Y
f ðtj Þ dx dt1 dti
16j6i
x¼0
s
g egx c ecs dx ds
x¼0 1
ti ¼0
1
g gþc
Z
1
Z
"
Ti ¼t1 þþti
ge t1 ¼0
1
x¼0 i Y j¼1
! xj ; xj þ g
gx
Y
xj e
xj tj
# dx dt1 dti
16j6i
ð5Þ
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where xj ¼ l þ jðg þ cÞ. The forwarded message arrival rate can thus be obtained from (1) and (5) as k f ¼ kn
B1 X i¼1
Probfforward j si gpi þ kf
BþN X1
Probfforward j si gpi :
ð6Þ
i¼1
Using (1) and (6), kf can be determined as follows. Starting with an initial ð1Þ ð1Þ guess of kf , we first derive the steady state probabilities pi using (1). From pi , ðjÞ fð1Þ k can be calculated using (6). This procedure is iterated until pi and kfðjÞ converge, and these quantities are used as estimates for pi and kf , respectively. In the following, we show the effects of the portable mobility rate g and the message expiration rate c on the forwarded message traffic load kf =l. The effect of the portable mobility rate g on the forwarded message traffic load kf =l can be seen in Fig. 5, where the message expiration rate c ¼ 0:001l, the buffer capacity B ¼ 10, and the overload-space capacity N ¼ 2. The figure shows that the forwarded message traffic load increases as the new message traffic load or the portable mobility rate increases. This is intuitively reasonable. Besides, it is seen that the forwarded message traffic load is insensitive to the new message traffic load kn =l under smaller portable mobility rate, say g 6 0:001l, and significantly increases as kn =l under larger portable mobility rate, say g P 0:1l. For example, when kn =l ¼ 0:9, the proportions of the forwarded message traffic load are about 0.17% and 20% of the new message traffic load if g ¼ 0:001l and g ¼ 0:1l, respectively. Hence, the forwarding effect of queued messages can not be ignored, especially in the networks with heavy traffic loads and highly mobile users. Fig. 6 plots the forwarded message traffic load kf =l for different message expiration rates c as a function of the new message traffic load kn =l, given that
Fig. 5. Forwarded message traffic load kf =l versus kn =l for different g.
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243
Fig. 6. Forwarded message traffic load kf =l versus kn =l for different c.
the portable mobility rate g ¼ 0:1l, the buffer capacity B ¼ 10, and the overload-space capacity N ¼ 2. The figure shows that the forwarded message traffic load decreases as the message expiration rate increases. This is due to the fact that as c increases the queued messages are more likely to be dropped, resulting in the decrease in the forwarded message traffic load. Another observation from Fig. 6 is that the forwarded message traffic load is less sensitive to c, especially when c is relatively small, say c 6 0:001l. For example, when kn =l ¼ 0:9, the forwarded message traffic load is increased from 0.183 at c ¼ 0:001l to 0.187 at c ¼ 0:0001l. This result is because c has a direct effect on the loads of queued messages but an indirect effect on that of forwarded messages. 2.2. Loss probability A message (newly arriving or forwarded) may be discarded for one of two reasons. The first is that the buffer occupancy (the overload-space occupancy) is greater than B 1 (N 1) when a new (forwarded) message arrives. The second is that a message, although accepted and waiting in the queue, fails to be transmitted within its timeout period and so is immediately removed from the queue. Also, consider the message mi arriving at state si . The message mi expires if s < x and s < Ti . Under the memoryless conditions and using (2)–(4), the probability that the message mi expires, can be expressed as Probfexpire Z Z j si g ¼ Probfs < x and s < Ti j si g 1
x
x¼0
s¼0
¼
Z
1
ti ¼0
fs ðsÞfx ðxÞ ds dx Z 1 Z Ti ¼t1 þþti t1 ¼0
s¼0
" fs ðsÞ
Y 16j6i
# f ðtj Þ ds dt1 dti
244
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¼
Z
1
Z
x¼0
Z
x
c ecs g egx ds dx
s¼0 1
Z
ti ¼0
¼
1
Z
ce t1 ¼0
c gþc
"
Ti ¼t1 þþti
1
cs
s¼0 i Y j¼1
Y
# xj e
xj tj
ds dt1 dti
16j6i
! xj ; xj þ c
ð7Þ
where xj ¼ l þ jðg þ cÞ. Using (7), the loss probability for the newly arriving messages in the SGSN can be expressed as Ln ¼
BþN X
pi þ
i¼B
B1 X
Probfexpire j si gpi
ð8Þ
i¼1
and for the forwarded messages it can be obtained as Lf ¼ pBþN þ
BþN X1
Probfexpire j si gpi ;
ð9Þ
i¼1
where pi can be calculated from (1). 2.3. Waiting time The waiting time of a message in an SGSN is defined as the time between the acceptance of such a message by the SGSN and its being transmitted. Again, consider the message mi arriving at state si . The message mi expires, is forwarded to a new SGSN, or is transmitted. From (5) and (7), the probability that the message mi is transmitted, can thus be expressed as Probftransmit j si g ¼ 1 ½Probfexpire j si g þ Probfforward j si g " ! i Y c xj ¼1 1 gþc x þc j¼1 j !# i Y g xj þ 1 ; gþc x þg j¼1 j
ð10Þ
where xj ¼ l þ jðg þ cÞ. Under the condition that the message mi is transmitted, the average waiting time of the message mi can be expressed as E½Ti j transmit j si ¼
E½Ti and transmit j si ; Probftransmit j si g
ð11Þ
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245
where Probftransmit j si g is given in (10), and E½Ti and transmit j si can be calculated from (5) and (7) as follows: E½Ti and transmit j si ¼ E½Ti and ð1 expire forwardÞ j si
Z Ti ¼t1 þþti Z 1 Z 1 c ¼ ðt1 þ þ ti Þ 1 fs ðsÞ ds g þ c s¼0 ti ¼0 t1 ¼0 # " Y Z Ti ¼t1 þþti g fx ðxÞ dx f ðtj Þ dt1 dti g þ c x¼0 16j6i
Z Ti ¼t1 þþti Z 1 Z 1 c ¼ ðt1 þ þ ti Þ 1 c ecs ds g þ c s¼0 ti ¼0 t1 ¼0 # " Y Z Ti ¼t1 þþti g gx xj tj g e dx xj e dt1 dti g þ c x¼0 16j6i
Z 1 Z 1 c cðt1 þþti Þ g gðt1 þþti Þ e e ¼ ðt1 þ þ ti Þ þ gþc gþc ti ¼0 t1 ¼0 " # " #" # i i Y X Y c x 1 j
xj exj tj dt1 dti ¼ g þ c j¼1 xj þ c x þc 16j6i j¼1 j " #" # i i Y X g xj 1 þ ; ð12Þ g þ c j¼1 xj þ g x þg j¼1 j where xj ¼ l þ jðg þ cÞ. Using (11) and (12), the waiting time for the newly arriving messages in the SGSN can be obtained as Wn ¼
B1 X
E½Ti j transmit j si pi
ð13Þ
i¼1
and for the forwarded messages it can be obtained as Wf ¼
BþN X1
E½Ti j transmit j si pi :
ð14Þ
i¼1
The average waiting time of a message in an SGSN, denoted by W , can thus be obtained from (13) and (14) as W ¼
kn n k þ kf
Wnþ
kf n k þ kf
W f:
ð15Þ
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3. Numerical results By using the analytical model presented in Section 2, this section investigates the optimal (smallest) value of the overload-space capacity N under various mobility and expiration parameters. This section also studies the effects of changing these parameters on the optimal value of N , the message loss probability, and the message waiting time. Fig. 7 depicts the loss probabilities for the newly arriving and the forwarded messages (Ln and Lf , respectively) versus the overload-space capacity N for different portable mobility rates g, where we assume the new message traffic load kn =l ¼ 1:0, the message expiration rate c ¼ 0:001l, and the buffer capacity B ¼ 10. The figure shows that the optimal value of N increases as g increases. For example, the optimal value of N is 3 if g ¼ 0:01l and the optimal value of N is 5 if g ¼ 0:1l. This phenomenon can be inferred from the following fact. As shown in Fig. 5, the forwarded message traffic load increases as g increases. Thus, in order to minimize Lf , N is expected to increase with increasing g. Fig. 7 also reveals that Ln and Lf decrease as g increases. This is due to the fact that as g increases the buffer occupancy times decrease, resulting in the decrease in the message queue length and, hence, the associated decreases in Ln and Lf . Fig. 8 shows the effect of the message expiration rate c on the optimal value of N and the message loss probability, where the new message traffic load kn =l ¼ 1:0, the portable mobility rate g ¼ 0:1l, and the buffer capacity B ¼ 10. The figure shows that the optimal value of N increases with decreasing c. For example, the optimal value of N is 5 if c ¼ 0:001l and the optimal value of N is 7 if c ¼ 0:0001l. This result is because the forwarded message traffic load increases as c decreases, as shown in Fig. 6. Another reason for this result is that
Fig. 7. Message loss probability versus N for different g.
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247
Fig. 8. Message loss probability versus N for different c.
as c decreases the buffer occupancy times increase, resulting in the increase in the message queue length. Thus, in order to minimize the loss probability for the forwarded messages, N is expected to increase with decreasing c. Another observation from Fig. 8 is that the loss probability for the newly arriving messages increases as c decreases, while the loss probability for the forwarded messages decreases as c decreases when N P 3. This phenomenon can be inferred from the following fact. When the message queue size is small, a message is discarded mainly due to the lack of buffer space. As c decreases the buffer occupancy times increase, resulting in the increase in the message queue length and, hence, the associated increase in the message loss probability. On the other hand, if the message queue size is large, message discarding happens mainly due to the expiration of the timeout period. In this case, the message loss probability decreases as c decreases. The effect of the portable mobility rate g on the message waiting time W can be seen in Fig. 9, where the message expiration rate c ¼ 0:001l, the overloadspace capacity N ¼ 2, and the buffer capacity B ¼ 10. The figure shows that the message waiting time decreases as g increases. This is due to the fact that as g increases the buffer occupancy times decrease, resulting in the associated decrease in the message waiting time. Fig. 9 also shows that the message waiting time increases as the new message traffic load increases. This finding is intuitive. Fig. 10 shows the message waiting time W for different message expiration rates c as a function of the new message traffic load kn =l, given that the portable mobility rate g ¼ 0:1l, the overload-space capacity N ¼ 2, and the buffer capacity B ¼ 10. Again, the figure shows that as the new message traffic load increases the message waiting time increases. The figure also shows that as c increases the message waiting time decreases. This result is because the buffer
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Fig. 9. Message waiting time versus kn =l for different g.
Fig. 10. Message waiting time versus kn =l for different c.
occupancy times decrease as c increases, resulting in the associated decrease in the message waiting time.
4. Conclusions This paper proposed an overload control scheme called the N -overload scheme for the GPRS/UMTS SMS networks. Besides, this paper presented an analytical model for the GPRS/UMTS SMS network using the N -overload
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249
scheme. With our model, the impact of the forwarding traffic in a GPRS/ UMTS SMS network can be effectively analyzed. The numerical results revealed that the forwarding effect of queued messages cannot be ignored, especially in the networks with heavy traffic loads and highly mobile users. On the basis of the analytical model, the optimal value of N can be numerically determined so as to minimize the loss probability for the forwarded messages and, thus, to prevent messages from being excessively delayed before being successfully delivered. This paper also studied the effects of changing the portable mobility and the message expiration rates on the optimal value of N . The numerical results showed that the optimal value of N increases as the portable mobility rate increases, and decreases as the message expiration rate increases.
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Overload control for short message transfer in GPRS/UMTS networks q Yieh-Ran Haung a
a,*
, Jan-Ming Ho
b
Department of Computer Science and Engineering, Yuan Ze University, 135 Yuan-Tung Rd., Chung-Li, Toayuan 320, Taiwan b Institute of Information Science, Academia Sinica, Taipei 115, Taiwan Received 12 June 2003; accepted 20 February 2004
Abstract In the General Packet Radio Service (GPRS)/Universal Mobile Telecommunications System (UMTS) short message service (SMS) network, the serving GPRS support node (SGSN) stores the 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 valid queueing time expires. Once the SGSN’s buffer is full, all incoming messages must be discarded and retransmitted later. Under this situation, the messages, especially the forwarded messages, suffer from a longer delay before being successfully delivered. To prevent messages from being excessively delayed, this paper proposes an SGSN overload control scheme called the N -overload scheme. According to this scheme, a newly arriving message is discarded if the buffer is full upon its arrival. A forwarded message, however, is queued in an overload space of size N. Taking the forwarding and the expiration effects of queued messages into account, this paper also develops an analytical model to study the performance for the SGSN using the N -overload scheme. On the basis of the analysis, the optimal value of N is numerically determined so that the loss probability for the forwarded messages is minimized. 2004 Elsevier Inc. All rights reserved.
q
This work was supported by NSC under contract 92–2213–E–155–035. Corresponding author. Fax: +886-34638850. E-mail addresses: [email protected] (Y.-R. Haung), [email protected] (J.-M. Ho). *
0020-0255/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2004.02.023
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Keywords: GPRS; UMTS; SMS; SGSN; Overload control
1. Introduction Global System for Mobile communications (GSM) short message service (SMS) has become the most successful wireless data service. GSM SMS allows mobile users to send and receive text-based messages of up to 160 characters. The recently introduced enhanced messaging service (EMS), which offers a combination of text, simple pixel-images, and melodies, can be seen as an extension of GSM SMS with each of its messages being handled as a series of concatenated SMS messages. This means that operators can continue to use and derive income from current GSM networks. However, it is crucial that operators ensure their infrastructure have the necessary capacity to handle the increase in message traffic, especially when multimedia messaging service (MMS) [1] arrives and takes off. MMS is a new global messaging standard that enables the transmission of messages with full content versatility, including text, images, audio, and video, between mobile devices and from applications to these devices. MMS can be used over the General Packet Radio Service (GPRS)/Universal Mobile Telecommunications System (UMTS) SMS network [2,3]. The GPRS/UMTS SMS network architecture is illustrated in Fig. 1. In this architecture, when a GPRS mobile station (MS) or a UMTS user equipment (UE) sends a short message, this message is delivered to an SMS interworking mobile switching center (SMS-IWMSC) via the serving GPRS support node (SGSN). The SMS-IWMSC passes this message to an SMS center (SM-SC). The SM-SC forwards the message to an SMS gateway MSC (SMS-GMSC). Upon receipt of the message, the SMS-GMSC interrogates the home location register (HLR) for routing information and sends the message to the appro-
Originating MS/UE SMSIWMSC
SGSN
HLR
SM-SC
Terminating MS/UE SGSN
SMSGMSC
Fig. 1. GPRS/UMTS SMS network architecture. (For color see online version.)
Y.-R. Haung, J.-M. Ho / Information Sciences 170 (2005) 235–249
MS/UE
SGSN
IWMSC
237
SM-SC
(1) Send RPDU (1) Forward RPDU (1) Forward RPDU (2) Send RPAU (2) Forward RPAU (3) Send RPSU
(2) Forward RPAU (3) Forward RPSU (3) Forward RPSU
Fig. 2. Mobile-originated short message transfer procedure.
priate SGSN. The SGSN then delivers the message to the terminating MS/UE. In the following, we elaborate on the mobile-originated and the mobile-terminated short message transfer procedures. 1.1. Mobile-originated The message flow of the mobile-originated short message transfer procedure is shown in Fig. 2, and is explained in the following steps. (1) The MS/UE forms a relay protocol data unit (RPDU) containing the short message submitted, the addresses of the terminating SM-SC and MS/UE, the Validity-Period indicating the time period for which the message is valid, and the Status-Report indicating if the originating MS/UE requests a delivery report. Then, the MS/UE sends the RPDU to the IWMSC through the SGSN. After receiving the RPDU, the IWMSC establishes a link with the addressed SM-SC and forwards the RPDU to the SM-SC. (2) Upon receipt of the RPDU, the SM-SC sends a relay protocol acknowledgement unit (RPAU) to the MS/UE via the IWMSC and the SGSN for confirming that the SM-SC has received the submitted short message. (3) If the Status-Report described in Step (1) indicates that the originating MS/ UE requests a delivery report, the SM-SC shall send a relay protocol status unit (RPSU) with the status of the submitted short message (e.g., successfully delivered or dropped) to the MS/UE. 1.2. Mobile-terminated Fig. 3 depicts the message flow of the mobile-terminated short message transfer procedure. Each step is explained as follows.
238
Y.-R. Haung, J.-M. Ho / Information Sciences 170 (2005) 235–249 GMSC
SM-SC
HLR
old SGSN
new SGSN
MS/UE
(1) Send RPDU (2) MAP-SENDROUTINGINFO-SM (2) MAP-SENDROUTINGINFO-SM-ACK (2) Forward RPDU (3) Forward RPDU (3) Forward RPDU
(5) Forward RPAU/RPEU
(5) Forward RPAU/RPEU
(4) Send RPAU/RPEU
(5) Forward RPAU/RPEU
Fig. 3. Mobile-terminated short message transfer procedure.
(1) The SM-SC forms an RPDU containing the short message to be delivered and the address of the terminating MS/UE, and then sends the RPDU to the GMSC. (2) When receiving the RPDU, the GMSC sends a MAP-SEND-ROUTINGINFO-SM message [4] to the HLR. If the HLR determines that the short message transfer request can be served, it returns a MAP-SEND-ROUTING-INFO-SM-ACK message with the SGSN address to the GMSC. The GMSC then forwards the RPDU to the SGSN indicated by the HLR. (3) The SGSN transfers the RPDU to the terminating MS/UE. Notice that the SGSN shall store the RPDU in a queue until it is successfully transferred to the MS/UE or its maximum queueing time expires. The maximum queueing time must be shorter than the Validity-Period described in Step (1) of Fig. 2. A queued message is forwarded to the new SGSN and is immediately removed from the waiting queue of the old SGSN, if the corresponding MS/UE leaves the service area of the old SGSN (i.e., the MS/UE initiates an inter-SGSN routing area update [5]) before the valid queueing time expires. If the forwarded message is discarded due to buffer overflow or is not successfully transferred to the MS/UE within the permitted time, the new SGSN returns an appropriate error to the SMS-GMSC through the old SGSN. (4) If the short message delivery was successful, the MS/UE sends an RPAU to the new SGSN. Otherwise, a relay protocol error unit (RPEU) with an appropriate cause is sent to the new SGSN. (5) If the RPAU was received within the valid time period, the new SGSN forwards the RPAU to the SM-SC via the old SGSN and the GMSC. Other-
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239
wise (i.e., the stored RPDU can not be successfully delivered to the MS/UE within the permitted time), the new SGSN removes the RPDU from the queue and returns an RPEU with an appropriate cause to the SM-SC. As mentioned above, the SGSN shall store the mobile-terminated message in a queue until it is successfully transferred to the MS/UE 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 MS/UE leaves the service area of the old SGSN before the valid queueing time expires. Once the SGSNs buffer is full, all incoming mobileterminated messages must be discarded and retransmitted from the SM-SC later. Under this situation, the messages, especially the forwarded messages, suffer from a longer delay before being successfully delivered. The purpose of overload control for short message transfer in an SGSN is therefore to protect forwarded messages against newly arriving ones so as to prevent forwarded messages from being excessively delayed, which is especially needed for multimedia messages. This paper proposes an SGSN overload control scheme called the N -overload scheme. According to this scheme, a newly arriving message is discarded if the buffer is full upon its arrival. A forwarded message, however, is queued in an overload space of size N . Taking the forwarding and the expiration effects of queued messages into account, this paper also develops an analytical model to study the performance for the SGSN using the N -overload scheme. On the basis of the analysis, the optimal (smallest) value of N is numerically determined so that the loss probability for the forwarded messages is minimized. The effects of changing mobility and expiration parameters on the optimal value of N are also studied. The paper is organized as follows. Section 2 presents the analytical model for the SGSN using the N -overload scheme. Section 3 shows some numerical results to investigate the optimal value of N under various mobility and expiration parameters, and to study the effects of changing these parameters on the optimal value of N . Finally, Section 4 concludes the paper.
2. The analytical model Each SGSN in a GPRS/UMTS SMS network is modelled by a continuoustime model with the following parameters and assumptions. • The buffer has capacity for B messages. • The overload space has capacity for N messages. • The newly arriving mobile-terminated messages are Poisson distributed with a rate of kn . A newly arriving message is discarded if the buffer occupancy is
240
• •
•
•
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B, while a forwarded message is discarded only when the overload-space occupancy is N . The transmission time of a message is exponentially distributed with a mean of l1. 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 exponentially distributed with a mean of 1c, as in [6–9]. 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. The forwarded messages are accepted as long as the buffer is not full, and are generated according to a Poisson distribution with a rate of kf . Notice that kf is correlated with other parameters (e.g., portable mobility, message transmission time, timeout period, etc.) and can be determined by an iterative method (see Section 2.1). The SGSN area residence time of a portable is exponentially distributed with a mean of 1g. Although the residence times are typically non-exponential in a particular mobile system, the analysis based on the simplified exponential assumption has been widely used [10–13] and does provide useful mean value information for the output measures.
The above queueing model can be described by a one-dimensional Markov chain with states si where i denotes the number of messages in buffer. Fig. 4 describes the state diagram. Let pi be the steady state probability for si . Using the Markov chain balance equations, the steady state probability is given by 8Q n f < ij¼1 k þk p0 ; if 1 6 i 6 B; xj f ð1Þ p i ¼ QB n f Qi k þk k : ; if B þ 1 6 i 6 B þ N ; p 0 j¼1 j¼Bþ1 xj xj PBþN where xj ¼ l þ jðg þ cÞ and i¼0 pi ¼ 1. In the following, general expressions will be derived to calculate the forwarded message arrival rate, the message loss probability, and the message waiting time in the SGSN. 2.1. Forwarded message arrival rate This section proposes an iterative method to determine the forwarded message arrival rate kf . Suppose that a message mi arrives at time t when the
Fig. 4. State diagram.
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241
SGSN is in state si . Consider the i outstanding messages that arrive at the SGSN earlier than mi . Among these i messages, the first leaves the SGSN (either the message is transmitted, expires, or is forwarded to a new SGSN) at time t þ ti ; the second leaves the SGSN at time t þ ti þ ti1 , and the ith message leaves the SGSN at time t þ ti þ ti1 þ þ t1 . Under the memoryless conditions, the probability density function for ti is given by f ðti Þ ¼ ½l þ iðg þ cÞe½lþiðgþcÞti :
ð2Þ
Let Ti denote the time elapsed before the message mi is transmitted (i.e., Ti ¼ t1 þ t2 þ þ ti ). Also, let s be the timeout period for mi , and x be the period between the arrival of mi and the time when the corresponding portable leaves the service area of the SGSN. The probability density functions of s and x can be expressed as fs ðsÞ ¼ cecs
ð3Þ
fx ðxÞ ¼ gegx ;
ð4Þ
and
respectively. As mentioned earlier, a queued message (within its timeout period) is forwarded to the new SGSN if the corresponding portable leaves the service area of the old SGSN before being transmitted. That is, the message mi is forwarded to a new SGSN if x < s and x < Ti . Thus, the probability that the message mi is forwarded to a new SGSN can be expressed as Probfforward j si g ¼ Probfx < s and x < Ti j si g Z 1Z s fx ðxÞfs ðsÞ dx ds ¼ s¼0
Z
x¼0 1
Z
ti ¼0
¼
Z
1
Z
t1 ¼0
Z
s¼0
¼
Z
Ti ¼t1 þþti
fx ðxÞ
Y
f ðtj Þ dx dt1 dti
16j6i
x¼0
s
g egx c ecs dx ds
x¼0 1
ti ¼0
1
g gþc
Z
1
Z
"
Ti ¼t1 þþti
ge t1 ¼0
1
x¼0 i Y j¼1
! xj ; xj þ g
gx
Y
xj e
xj tj
# dx dt1 dti
16j6i
ð5Þ
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where xj ¼ l þ jðg þ cÞ. The forwarded message arrival rate can thus be obtained from (1) and (5) as k f ¼ kn
B1 X i¼1
Probfforward j si gpi þ kf
BþN X1
Probfforward j si gpi :
ð6Þ
i¼1
Using (1) and (6), kf can be determined as follows. Starting with an initial ð1Þ ð1Þ guess of kf , we first derive the steady state probabilities pi using (1). From pi , ðjÞ fð1Þ k can be calculated using (6). This procedure is iterated until pi and kfðjÞ converge, and these quantities are used as estimates for pi and kf , respectively. In the following, we show the effects of the portable mobility rate g and the message expiration rate c on the forwarded message traffic load kf =l. The effect of the portable mobility rate g on the forwarded message traffic load kf =l can be seen in Fig. 5, where the message expiration rate c ¼ 0:001l, the buffer capacity B ¼ 10, and the overload-space capacity N ¼ 2. The figure shows that the forwarded message traffic load increases as the new message traffic load or the portable mobility rate increases. This is intuitively reasonable. Besides, it is seen that the forwarded message traffic load is insensitive to the new message traffic load kn =l under smaller portable mobility rate, say g 6 0:001l, and significantly increases as kn =l under larger portable mobility rate, say g P 0:1l. For example, when kn =l ¼ 0:9, the proportions of the forwarded message traffic load are about 0.17% and 20% of the new message traffic load if g ¼ 0:001l and g ¼ 0:1l, respectively. Hence, the forwarding effect of queued messages can not be ignored, especially in the networks with heavy traffic loads and highly mobile users. Fig. 6 plots the forwarded message traffic load kf =l for different message expiration rates c as a function of the new message traffic load kn =l, given that
Fig. 5. Forwarded message traffic load kf =l versus kn =l for different g.
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243
Fig. 6. Forwarded message traffic load kf =l versus kn =l for different c.
the portable mobility rate g ¼ 0:1l, the buffer capacity B ¼ 10, and the overload-space capacity N ¼ 2. The figure shows that the forwarded message traffic load decreases as the message expiration rate increases. This is due to the fact that as c increases the queued messages are more likely to be dropped, resulting in the decrease in the forwarded message traffic load. Another observation from Fig. 6 is that the forwarded message traffic load is less sensitive to c, especially when c is relatively small, say c 6 0:001l. For example, when kn =l ¼ 0:9, the forwarded message traffic load is increased from 0.183 at c ¼ 0:001l to 0.187 at c ¼ 0:0001l. This result is because c has a direct effect on the loads of queued messages but an indirect effect on that of forwarded messages. 2.2. Loss probability A message (newly arriving or forwarded) may be discarded for one of two reasons. The first is that the buffer occupancy (the overload-space occupancy) is greater than B 1 (N 1) when a new (forwarded) message arrives. The second is that a message, although accepted and waiting in the queue, fails to be transmitted within its timeout period and so is immediately removed from the queue. Also, consider the message mi arriving at state si . The message mi expires if s < x and s < Ti . Under the memoryless conditions and using (2)–(4), the probability that the message mi expires, can be expressed as Probfexpire Z Z j si g ¼ Probfs < x and s < Ti j si g 1
x
x¼0
s¼0
¼
Z
1
ti ¼0
fs ðsÞfx ðxÞ ds dx Z 1 Z Ti ¼t1 þþti t1 ¼0
s¼0
" fs ðsÞ
Y 16j6i
# f ðtj Þ ds dt1 dti
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¼
Z
1
Z
x¼0
Z
x
c ecs g egx ds dx
s¼0 1
Z
ti ¼0
¼
1
Z
ce t1 ¼0
c gþc
"
Ti ¼t1 þþti
1
cs
s¼0 i Y j¼1
Y
# xj e
xj tj
ds dt1 dti
16j6i
! xj ; xj þ c
ð7Þ
where xj ¼ l þ jðg þ cÞ. Using (7), the loss probability for the newly arriving messages in the SGSN can be expressed as Ln ¼
BþN X
pi þ
i¼B
B1 X
Probfexpire j si gpi
ð8Þ
i¼1
and for the forwarded messages it can be obtained as Lf ¼ pBþN þ
BþN X1
Probfexpire j si gpi ;
ð9Þ
i¼1
where pi can be calculated from (1). 2.3. Waiting time The waiting time of a message in an SGSN is defined as the time between the acceptance of such a message by the SGSN and its being transmitted. Again, consider the message mi arriving at state si . The message mi expires, is forwarded to a new SGSN, or is transmitted. From (5) and (7), the probability that the message mi is transmitted, can thus be expressed as Probftransmit j si g ¼ 1 ½Probfexpire j si g þ Probfforward j si g " ! i Y c xj ¼1 1 gþc x þc j¼1 j !# i Y g xj þ 1 ; gþc x þg j¼1 j
ð10Þ
where xj ¼ l þ jðg þ cÞ. Under the condition that the message mi is transmitted, the average waiting time of the message mi can be expressed as E½Ti j transmit j si ¼
E½Ti and transmit j si ; Probftransmit j si g
ð11Þ
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245
where Probftransmit j si g is given in (10), and E½Ti and transmit j si can be calculated from (5) and (7) as follows: E½Ti and transmit j si ¼ E½Ti and ð1 expire forwardÞ j si
Z Ti ¼t1 þþti Z 1 Z 1 c ¼ ðt1 þ þ ti Þ 1 fs ðsÞ ds g þ c s¼0 ti ¼0 t1 ¼0 # " Y Z Ti ¼t1 þþti g fx ðxÞ dx f ðtj Þ dt1 dti g þ c x¼0 16j6i
Z Ti ¼t1 þþti Z 1 Z 1 c ¼ ðt1 þ þ ti Þ 1 c ecs ds g þ c s¼0 ti ¼0 t1 ¼0 # " Y Z Ti ¼t1 þþti g gx xj tj g e dx xj e dt1 dti g þ c x¼0 16j6i
Z 1 Z 1 c cðt1 þþti Þ g gðt1 þþti Þ e e ¼ ðt1 þ þ ti Þ þ gþc gþc ti ¼0 t1 ¼0 " # " #" # i i Y X Y c x 1 j
xj exj tj dt1 dti ¼ g þ c j¼1 xj þ c x þc 16j6i j¼1 j " #" # i i Y X g xj 1 þ ; ð12Þ g þ c j¼1 xj þ g x þg j¼1 j where xj ¼ l þ jðg þ cÞ. Using (11) and (12), the waiting time for the newly arriving messages in the SGSN can be obtained as Wn ¼
B1 X
E½Ti j transmit j si pi
ð13Þ
i¼1
and for the forwarded messages it can be obtained as Wf ¼
BþN X1
E½Ti j transmit j si pi :
ð14Þ
i¼1
The average waiting time of a message in an SGSN, denoted by W , can thus be obtained from (13) and (14) as W ¼
kn n k þ kf
Wnþ
kf n k þ kf
W f:
ð15Þ
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3. Numerical results By using the analytical model presented in Section 2, this section investigates the optimal (smallest) value of the overload-space capacity N under various mobility and expiration parameters. This section also studies the effects of changing these parameters on the optimal value of N , the message loss probability, and the message waiting time. Fig. 7 depicts the loss probabilities for the newly arriving and the forwarded messages (Ln and Lf , respectively) versus the overload-space capacity N for different portable mobility rates g, where we assume the new message traffic load kn =l ¼ 1:0, the message expiration rate c ¼ 0:001l, and the buffer capacity B ¼ 10. The figure shows that the optimal value of N increases as g increases. For example, the optimal value of N is 3 if g ¼ 0:01l and the optimal value of N is 5 if g ¼ 0:1l. This phenomenon can be inferred from the following fact. As shown in Fig. 5, the forwarded message traffic load increases as g increases. Thus, in order to minimize Lf , N is expected to increase with increasing g. Fig. 7 also reveals that Ln and Lf decrease as g increases. This is due to the fact that as g increases the buffer occupancy times decrease, resulting in the decrease in the message queue length and, hence, the associated decreases in Ln and Lf . Fig. 8 shows the effect of the message expiration rate c on the optimal value of N and the message loss probability, where the new message traffic load kn =l ¼ 1:0, the portable mobility rate g ¼ 0:1l, and the buffer capacity B ¼ 10. The figure shows that the optimal value of N increases with decreasing c. For example, the optimal value of N is 5 if c ¼ 0:001l and the optimal value of N is 7 if c ¼ 0:0001l. This result is because the forwarded message traffic load increases as c decreases, as shown in Fig. 6. Another reason for this result is that
Fig. 7. Message loss probability versus N for different g.
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247
Fig. 8. Message loss probability versus N for different c.
as c decreases the buffer occupancy times increase, resulting in the increase in the message queue length. Thus, in order to minimize the loss probability for the forwarded messages, N is expected to increase with decreasing c. Another observation from Fig. 8 is that the loss probability for the newly arriving messages increases as c decreases, while the loss probability for the forwarded messages decreases as c decreases when N P 3. This phenomenon can be inferred from the following fact. When the message queue size is small, a message is discarded mainly due to the lack of buffer space. As c decreases the buffer occupancy times increase, resulting in the increase in the message queue length and, hence, the associated increase in the message loss probability. On the other hand, if the message queue size is large, message discarding happens mainly due to the expiration of the timeout period. In this case, the message loss probability decreases as c decreases. The effect of the portable mobility rate g on the message waiting time W can be seen in Fig. 9, where the message expiration rate c ¼ 0:001l, the overloadspace capacity N ¼ 2, and the buffer capacity B ¼ 10. The figure shows that the message waiting time decreases as g increases. This is due to the fact that as g increases the buffer occupancy times decrease, resulting in the associated decrease in the message waiting time. Fig. 9 also shows that the message waiting time increases as the new message traffic load increases. This finding is intuitive. Fig. 10 shows the message waiting time W for different message expiration rates c as a function of the new message traffic load kn =l, given that the portable mobility rate g ¼ 0:1l, the overload-space capacity N ¼ 2, and the buffer capacity B ¼ 10. Again, the figure shows that as the new message traffic load increases the message waiting time increases. The figure also shows that as c increases the message waiting time decreases. This result is because the buffer
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Fig. 9. Message waiting time versus kn =l for different g.
Fig. 10. Message waiting time versus kn =l for different c.
occupancy times decrease as c increases, resulting in the associated decrease in the message waiting time.
4. Conclusions This paper proposed an overload control scheme called the N -overload scheme for the GPRS/UMTS SMS networks. Besides, this paper presented an analytical model for the GPRS/UMTS SMS network using the N -overload
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scheme. With our model, the impact of the forwarding traffic in a GPRS/ UMTS SMS network can be effectively analyzed. The numerical results revealed that the forwarding effect of queued messages cannot be ignored, especially in the networks with heavy traffic loads and highly mobile users. On the basis of the analytical model, the optimal value of N can be numerically determined so as to minimize the loss probability for the forwarded messages and, thus, to prevent messages from being excessively delayed before being successfully delivered. This paper also studied the effects of changing the portable mobility and the message expiration rates on the optimal value of N . The numerical results showed that the optimal value of N increases as the portable mobility rate increases, and decreases as the message expiration rate increases.
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