AN EFFICIENT SEQUENTIAL PAGING TECHNIQUE USING FEEDBACK STRATEGY N. Banerjee*, D. Saha*, P. S. Bhattacharya+, and A. Mukherjee** *Department of Computer Science & Engg. ,Jadavpur University, Calcutta 700 032, India, E-mail:
[email protected] +Department of telecommunications, Calcutta, India. **PricewaterhouseCoopers Ltd., Salt Lake Calcutta 700 091, India.
Abstract In this paper, we consider a heuristic approach to reduce latency for mobile tracking in a city area. Our solution is based on the idea of parallelo-sequential paging, using mobility parameters of mobile units. Some design issues, based on specific cell layouts to get enhanced performance in terms of paging delay and call blocking, are also considered. The proposed algorithms employ breadth first search (BFS) strategies for different depths of search, with the direction of motion taken as feedback. It has been found that better delay performances are exhibited when the previous direction of motion of mobile units is taken as a feedback in calculating the current direction of motion. Keywords Paging, Breadth first search (BFS), Drift, Mobility Pattern, Feedback, Blocking Probability. Introduction A group of base stations (BS) [1] covering the service area and interconnected by a fixed backbone network through switches constitutes a conventional cellular network [1]. The coverage area of BS is referred to as a cell. The mobile subscribers (MS) [1], are connected to a BS via wireless links. Locating an MS is required in order to establish a connection with the MS having an incoming call. To facilitate this process, the network is divided into multiple location areas (LA) comprising usually more than one cell. A mobile switching center (MSC) [1] is the central coordinating element for all cell sites within an LA.
The paging strategies are implemented in this level since it is the job of a MSC to determine the cells to be paged to track a MS having an incoming call. There are additionally two databases [1] – home location register (HLR) and visitor location register (VLR) which also helps in tracking. When an MS enters a new location area, it performs a location update. It may also update its location within the LA from time to time. Paging strategies can be broadly classified into two categories, namely parallel and sequential [4]. The conventional (GSM) paging strategy uses the parallel or broadcasting technique i.e., all the cells in an LA are paged simultaneously for tracking. This method is most efficient in terms of latency (paging delay). However, bandwidth requirement is maximum in this scheme because every cell in the LA broadcasts the paging message. On the other hand, a sequential strategy [2, 4], which pages the cells one at a time in some predetermined order, provides the best utilization in terms of bandwidth at the cost of paging delay. To get a trade-off between these two strategies, a parallel-o-sequential scheme has also been proposed that pages the cells in cluster [3]. However, they consider only four directions for MS movement in a Manhattan City model. Similar to [2], we have tried in [8] to look into a sequential paging strategy that uses the call statistics and mobility pattern of the MSs [5]. The idea was to develop a paging strategy where the cell having the highest probability of an MS being resident in it is paged before the others. Taking registration cell number and the initial polar coordinate of an MS into
consideration, in [8] we have used greedy search algorithms to reduce latency as well as to increase the hit ratio. The algorithms have been implemented using both DFS and BFS strategies for different depths of search. In [9], we have tried to develop a parallel-o-sequential scheme and proposed a suitable size for groups of cells to be paged at a time. Since this paging has been done in-groups, considerable improvement in terms of delay has been achieved with respect to our previous work [8]. In this paper, we have tried to improve our earlier scheme [9] by taking direction into feedback and studying the errors in terms of blocking probability in order to minimize it. Comparative study between them reveals that this feedback strategy help in achieving better results in terms of hit ratio. This study also helps in selecting a desirable search pattern depending on the required call blocking probability (or, quality of service). System Model To implement our plan we have developed a model. In our model, each cell edge has been mapped to integers 0 through 5 in anti-clockwise order. Using these cell edge values, we can represent the entire LR area in the form of an (m x 6) matrix, where m is the number of cells in the LR area. The matrix X can be written as, x11 x12
X=
x16
xij xm1
xm2
xm6
where xij, i = 1 ... m & j = 1 ... 6, gives the cell number of the cell which is adjacent to the cell i at the edge j. This matrix X can be used to give the shape of any LR area. Next, we consider the mobility parameters of MSs within the LA. An important aspect of mobility is the drift, which can be defined as the change in direction at a particular instant with respect to the previous direction [5]. This drift is a continuous variable
between –180 to +180, which is assumed to follow a Gaussian distribution [6] with mean 0 for vehicular MSs. This is because a vehicular MS can be assumed to move in a straight-line and thus drift of 0 is most probable than the drifts of other denominations. This continuous case can be elegantly mapped to the discrete case in the following manner. Since the drift can vary from +180 to –180 with mean 0 and because the Gausssian distribution is symmetric about the mean, the drift of 0 is the most probable case, i.e. the edge opposite to the entry edge, say p, would be the most likely exit edge. Now the edges immediately adjacent to p correspond to a drift greater than +30 or less than –30. Consequently, by the distribution, this drift will be less probable than the earlier case, and as such the edges will also be less likely to be the exit edge compared to the exactly opposite edge. This way we can order all the six edges while considering the motion of the MS. The call rate is assumed to follow a Poisson distribution with mean µ calls/hr. The inter-arrival time between successive calls therefore follows a negative exponential distribution. Background The proposed sequential paging strategy is an application of the Breadth First Search (BFS) [7] technique, as used in graph search, for paging in wireless cellular networks. As we have mentioned earlier, whenever an MS enters an LA it updates its location, i.e., the cell number in which it resides is recorded. Additionally, for the purpose of our paging scheme we also record the cell edge number through which the MS had entered the cell. Now, when a call comes for an MS, we have the previous two data as the starting point. From the distribution of the drift, the probability that the MS goes in a straight line is the highest and its chance of deviation progressively decreases. Hence, knowing the edge through which it had entered the registration cell, the edge just opposite to the entry edge is the edge with the highest probability of exit. So we can find the adjacent cell numbers from our topology matrix, where it may be present with the
highest probability. This is the case if the call rate is very high or the average velocity is low, i.e., we search cells at depth 1 or the adjacent cells. Therefore, for the following layout, the search sequence, with depth parameter as 1, will be {2, 3, 4, 5, 6, 7, 1}.
2
1.2 Select the Registration Cell to be the current cell (CC) or the cell for which the next probable cell is searched.
1.4 If N does not exist { dequeue CC from the queue, [7]
1 7
1.1 Select a depth, which is a designer's choice.
1.3 If all the adjacent cells are not checked, find N the next highest probable cell.
3 5
1. Generate the paging sequence as follows.
4 6
mark CC, add it to the paging sequence. } Else { enqueue CC to the queue, [7]
Figure 1: An MS has entered into cell 1 from cell 7
assign N to CC. } 1.5 If queue not empty, goto 1.3
For different average velocities and call rates, the position of the MS within the LA will change randomly. So, in order to track the MS, we start from the edge of entry of the registration cell. Selecting a depth, we can first generate the search sequence and then page each cell from the sequence at each paging cycle. Here, depth is an important criterion, which sets a bound on the number of cells the MS is expected to cross during the period between the last registration and the current call request. So the highest probability of residence will be at a cell which is at a distance of (d * 2R) from the registration cell and in straight line from the entry edge in the direction of motion. Thus, this should be the first cell to be paged. The direction of motion is obtained as a feedback
2. Start from the beginning of the paging sequence. 3. Select the next group of suitable number of cells from the paging sequence. 4. Search the selected cells for the desired MS. 5. If the MS is not found, goto 3. 6. For every 500 searches check the difference of the mean blocking ratio with that of immediately previous 500 searches. If it is greater than a predetermined very small value then repeat the entire sequence for another 500 iterations. Simulation Aspects
Paging Strategy with feedback
The first thing about simulation is the generation of the motion of the MS within the LA. For this we have assumed an average velocity of 50 kmph for the MS and used the call rate between 1 to 5 calls/hr. The call statistics, velocity and cell radius can be combined to give the maximum number of cells crossed. These cells are selected randomly pertaining to the LA and if handoff situation arises those cases are left out of the simulation sample.
We briefly describe the algorithm in this section. It is simple and easy to implement. Details of the algorithm can be found in [8] and [9].
Assuming delay per paging cycle to be small, for the entire search sequence the MS is bound to reside in the cell that was generated by the above technique.
The above scheme generates a sequential paging sequence. In order to get a parallelo-sequential scheme certain number of cells from the sequence can be paged at a time
Next, we are applying the search algorithm to generate the paging sequence. Given the entry edge i, the maximum probable exit edge is, P = [ i + #edges/2] % #edges = [ i + 3] % 6. The next probable edges of exit are in the order as below. { [ P + 1]% 6 ; [P + (6-1)]% 6 ; [ P + 2]% 6 ; [P + (6-2)]% 6 ; [ P + 3]% 6 } . Corresponding to an exit edge the adjacent cell can be found from the topology matrix. Results and Discussion To study the paging algorithms, let us consider the following performance parameters: S = the expected number of times that an MS is paged before discovery. B = percentage of calls blocked = Ratio of the number of times that the MS could not be tracked by the algorithm to the total number of times that the MS has been paged.
3. Average Velocity for Ms has been taken as 50 kmph. Simulation I The parameters for this simulation are: •
The number of cells present in the LA is 100.
•
The maxspan, D is 16.
•
The group size is taken as 6 according to [9].
Results of this simulation are similar to [9] excepting that the simulation was performed with a set of 500 MSs whereas here simulation has been performed with a single MS for 500 times. From this table, we observe that to get better hit ratio i.e. reduced chance of blocked calls, we must increase the depth factor, d. This, however increases the expected number of cells paged before discovery i.e. the % decrease in signaling load decreases. Thus, there must be a tradeoff between S and B while selecting depth factor. Simulation II
The lesser the paging delay or latency (S) and blocking ratio (B), more efficient is the algorithm. For the conventional paging method, these two measures can be easily estimated as, the paging delay to be unity and blocking ratio zero. Another useful measure for analyzing the algorithm is,
This has the same parameters as in Simulation I. Here direction and error in blocking probability are taken as feedback. The acceptable error taken is of the order of 10-4. Results are again shown in Table I for comparison with the search technique without feedback.
% Decrease in signaling load = (Sconv - Sseq ) / Sconv .
From Table I it is evident that blocking ratio gets reduced appreciably with the introduction of feedback strategy particularly for lower values of search depths.
For the purpose of our analysis, we introduce a key parameter related to the layout, which we call maxspan. The maxspan, D is defined to be the maximum number of cells that an MS can cross in an LA moving linearly. In the following discussions, the outcome of some simulation experiments performed with our system is presented. All these simulation runs have been executed with the following assumptions: 1. Layout of the cells considered has been taken as that in a city area model. 2. Radius of each cell has been assumed to be 4 km.
We now discuss how to choose ‘d’ suitably for a given maxspan D of the layout. The results in Table I has D=16. In Fig 2, we have plotted the relative percentage decreases of the signaling load and the blocking rate at different depths. From the figure, we can set a bound on the selection of ‘d’ as, D/2 ≤ d ≤ 3D/4 In this range, block ratio is less than 1%, whereas decrease in signaling load is between 84% and 88%.
Table I City Area Cell Layout with 100 cells Paging without feedback
#
Paging with feedback
S
G
B
S
G
B
1
0.69
99.31
4.80
1.17
98.83
0.07
2
1.54
98.46
3.60
3.16
96.04
0.06
3
2.70
97.30
1.80
5.49
94.51
0.06
4
4.07
95.93
1.60
6.33
93.67
0.05
5
5.60
94.40
1.40
6.50
93.50
0.03
6
7.24
92.76
0.80
6.67
93.33
0.03
7
8.43
91.57
0.80
9.50
90.50
0.02
8
9.57
90.43
0.60
10.83
89.17
0.01
9
10.71
89.29
0.40
14.15
85.85
0.01
10
11.79
88.21
0.01
15.24
84.76
0.00
11
12.92
87.08
0.01
15.70
84.30
0.00
12
14.03
85.97
0.00
15.96
84.04
0.00
13
14.98
85.02
0.00
16.04
83.99
0.00
14
15.77
84.23
0.00
16.64
83.98
0.00
15
16.39
83.61
0.00
16.70
83.97
0.00
# gives search depth value; S is mean paging delay ; G is % decrease in signaling load; B is % of calls blocked
N o .
o f
C e lls
=
1 0 0
120 100 80 60 40 20
d e p t h
% %
15
13
11
9
7
5
3
1
0
f a c t o r s
d e c r e a s e in s ig n a lin g o f c a lls b lo c k e d
lo a d
Fig 2. % decrease in signaling load vis-à-vis blocking rate at different depths for cell layout with maxspan of 16 cells (blocking rate has been magnified by a scale of 100 for the purpose of comparison)
This substantial improvement in terms of blocking ratio has been achieved due to the feedback scheme. Thus, in this working range both the blocking ratio and the paging delay are found to be tolerable. With increasing D, this bound will be even more useful. Conclusion In [9], we have shown BFS based parallel-osequential paging strategy with a depth bound in the range [D/2,3D/4] gives a hit ratio comparable to that of conventional technique at acceptable latency value and some gains in terms of signaling load. In this paper, we have shown that further decrease in terms of blocking ratio can be achieved by introducing feedback strategy. References [1] Steele, R. 1992 Mobile Radio Communications. Pentech Press.
[2] Rezaiifar, Ramin and Makowski, Armand M. 1997 From Optimal Search Theory to Sequential Paging in Cellular Networks. IEEE Journal on Selected Areas in Communications, Vol. 15, No. 7, September 1997. [3] Abutaleb, Ahmed. and Li, Victor O. K. 1997. Paging strategy optimization in personal communication systems. Wireless Networks 3 195-204. [4] Bhattacharya, P.S. Saha, D. Mukherjee, A. 1999. Optimization of Update and Paging Costs for Location Area Planning in a PCSN. Global Communications, Vol.10 ITU-D, September 1999. [5] Zonoozi, Mahmood M. and Dassanayake, Prem. 1997. User Mobility Modeling and Characterization of Mobility Patterns. IEEE Journal on Selected Areas in Communications, Vol. 15, No. 7, September 1997. [6] Trivedi, Kishor S. Probability & Statistics with Reliability, Queuing and Computer Science Applications. Prentice-Hall International, Inc., Englewood Cliffs.
