Scheduling for ordered query services in
multi-channel data broadcast systems
Yu-Hsien Lin, Yi-Syuan Jiang, and Wei-Mei Chen
Department of Electronic EngineeringNational Taiwan University of Science and Technology Taipei 106, Taiwan
{M9602109, B9630132, wmchen}@mail.ntust.edu.tw
Abstract—In wireless mobile environments, the bandwidth and client capability are limited. Data broadcasting is an efficient and scalable method to disseminate information to a large amount of mobile clients. In recent years, several research has engaged in scheduling dependent data on multiple broadcast channels. However, most of the previous research focused on unordered queries and only few of them on ordered queries. In this paper, we study the problem of data allocation for ordered queries on multiple broadcast channels and devise an efficient algorithm based on a local search strategy. The experimental results show that the proposed algorithm outperforms the existing algorithms when the query distribution is known. Moreover, our algorithm with minor modification can also be applied efficiently when the query distribution is unknown.
Keywords: data broadcasting, data scheduling, multiple chan-nels, wireless mobile networks
I. INTRODUCTION
Nowadays, due to the advances in wireless networks, people can access information by portable devices such as laptops, PDA, and smart phones in daily life. In this scenario, there are various media contents provided, including stock information, weather forecast, traffic report, and news [7][21]. Because the bandwidth and client capability are restricted[15], disseminat-ing information efficiently under limited resources conditions is an important issue in wireless mobile environments.
Data broadcasting is an efficient and scalable method to disseminate information for a large amount of mobile clients. Typically, there are three kinds of data broadcast models: the pull-based model, the push-based model, and the hybrid broad-cast model [13][15]. In the pull-based model (also refer to on-demand broadcast), clients send requests to the server and keep listening broadcast channels for the data requested. In the push-based broadcast, servers broadcast all data periodically and clients retrieve the data needed when it is broadcasted. Based on this model, the scheme of broadcast disks [1][2] schedules data on single channel by the access probability in which hot data items are broadcast more frequently. The hybrid broadcast model applies pull-based broadcast and push-based broadcast in different situations. For instance, the hybrid approach suggested in [26] broadcasts popular data by the push-based method and others by the pull-based model.
In most applications, clients request several kinds of data in a query, which is called complex query (or dependent data). In general, complex queries are categorized into two types:
unordered queries and ordered queries. Data in unordered queries does not have to be retrieved in certain order. The QEM algorithm [5] schedules unordered queries according to the access probability. This problem is proved to be NP-hard in [6]. Later, the MQEM algorithm is suggested in [13] which improves the performance of the QEM algorithm by using a weighted undirected graph. Another scheduling algorithm is proposed by using tree structures to allocate data on multiple channels [23]. On the other hand, a genetic algorithm in [8] is proposed to solve the data scheduling problem for unordered queries on multiple channels.
In ordered query environments, data items are associated such that objects need to be retrieved in sequential order. In the systems with only one single channel, there are some researches on allocating ordered queries by various directed graphes and data structures in [4][14][25]. For multiple chan-nel environments, Huang and Chen [10] use a genetic al-gorithm to allocate ordered data on multiple channels. The algorithms, MPPA, RMPPA, and CMPPA [17][18] arrange data items on multiple channels by exploiting DAG and heaps. Given the query distribution, Hung and Chen present the MULS framework [11] to schedule sequential data broad-casting. The MULS algorithm contains two stages: OLS and BASIC. The OLS algorithm checks backward or forward for two consecutive items item to allocate better placement. The BASIC algorithm is proposed to schedule the broadcast program by comparing all possible pairs of data and then exchanging them for the best arrangement. Although MULS can adjust the broadcast program for less access time, it takes much time to evaluate possible solutions. In addition, the broadcast scheduling problem with data replication is studied for ordered queries in [9].
Most researches consider the environment is static and the exact request distribution is known. However clients may sent queries in any time or new clients might join in the system spontaneously. Under such dynamic conditions, the related query distribution is hard to obtain in advance. In this paper, we allocate ordered queries on multiple channels when the query distribution is unknown. Our algorithm schedules the ordered data item in a query and adjusts the scheduled data item when they appear in the unscheduled query again. We first exam and evaluate some promising data items, and then exchange the broadcast sequence to reduce the average access
time. Meanwhile, when the query distribution is known, our algorithm takes less average access time and reduces execution time, compared to the MULS algorithm.
The rest of this paper is organized as follows. Section 2 describes the environment, preliminaries, and analytical models. In Section 3, the proposed algorithm is present and brief examples are given. The simulation results are shown in Section 4. Finally, this paper concludes with Section 5.
II. DEFINITION
In this section, we introduce the problem definition and some notations used in this paper.
A. Environment
The environment of this paper is shown in Fig. 1. The clients send their queries to the server. Every query contains several data items which are equal in size and are ordered. When the server receives queries, it starts to schedule the broadcast program and then follows the program to broadcast data cycle by cycle. On the other hand, clients listen to all channels and download data in order when the needed data is broadcasted. If one broadcast cycle is finished and there are new data requested, the server stops broadcasting and adjusts the broadcast program. Once the broadcast program is altered, the sever informs all clients in this system and starts to broadcast by the new broadcast program.
Server
…
K Broadcast Channels
Client 1 Client 2 Client i Broadcast … d1 d2 d3 d4 … … d5 d6 d7 d8 Request <d1, d6, d8> <d5, d4, d3, d7> <d2, d8> Query List q1:<d1, d6, d8> q2:<d5, d4, d3, d7> … qi:<d2, d8> …
Query1 Query2 Query i … …
… … Scheduler
Fig. 1. The environment of broadcasting ordered queries on multiple channels.
B. Notations
Suppose that the number of channels in the system is K for K ≥ 1 and there are a set of N distinct data items D, where D = {d1, d2, . . . , dN} and each data item di is equal
in size for 1 ≤ i ≤ N . Let Q denote a set of all ordered queries and Q = {q1, q2, . . . , qM} where M is the number
of ordered queries requested from clients. Each ordered query contains several data items and these data items need to be downloaded in order. Let q be a query in Q, q(j) be the jth data item in q, nq be the number of data items requested in
q, and fq be the access probability of q.
Assume that the length of broadcast cycle is L, which means that for each cycle there are L data items to be broadcast in a channel. Since every data item is just broadcast once and every channel broadcasts the same number of data, we have L = dN/Ke. The broadcast program is recorded as a K × L matrix P . For the data item di, let K(di) be the channel that di
is arranged and L(di) be the position of di in channel K(di).
Thus P [K(di)][L(di)] = di. For the reader’s convenience, all
of the symbols in this paper are summarized in Table I.
TABLE I
DESCRIPTION OF PARAMETERS. Parameters Description
D a set of all data items N the number of data items in D di the ith data items in D, 16 i 6 N
Q a set of ordered queries
M the number of ordered queries in Q q an ordered query in Q
nq the number of data items requested in q
fq the access probability of q
K the number of broadcast channels L the length of a broadcast cycle P the broadcast program K(di) the channel of di
L(di) the position of diin channel K(di)
For example, consider that the set of all data items D = {d1, d2, d3, d4, d5, d6}, the number of data items N = 6, and
Q = {q1, q2, q3}. The ordered queries profile is given in Table
II. If K = 2 and L = 3, three feasible broadcast programs are shown in Fig. 2.
TABLE II
EXAMPLE OF ORDERED QUERIES PROFILE. Probability Query Contents
0.5454 q1 < d1, d2, d3> 0.2727 q2 < d3, d4, d5, d6> 0.1818 q3 < d3, d4, d6> 1 2 3 1 d4 d5 d6 2 d1 d2 d3 (a) K 1 2 3 1 d4 d6 d5 2 d1 d2 d3 (b) 1 2 3 1 d4 d5 d3 2 d1 d2 d6 (c) K K L L L
Fig. 2. Three feasible broadcast programs.
C. Analytical Models
Herein we describe some related definitions, the more detailed discussions for ordered queries on multiple channels are studied in [10][11].
When each data item is equal in size and the download bandwidth is stable, the time of download each data item is the same. Let the time of download a data item be a unit of time. In the broadcast program P for two distinct data items
di and dj, the distance from dito dj, denoted by ∆(di, dj) is defined as follows: ∆(di, dj) = L(dj) − L(di) − 1, if L(dj) > L(di), L − L(di) + L(dj) − 1, otherwise. In particular, ∆(di, di) = 0.
Let TA(q) be the access time of query q; that is,
TA(q) = TS(q) + TW(q) + TR(q),
where the start-up time TS(q) is the time between the client
starts listening and the client receives the first data item of query. The waiting time TW(q) is defined by TW(q) =
Pnq−1
j=1 ∆(q(j), q(j + 1)). The retrieval time TR(q) is the time
that the client spends to download all data items.
Consider the broadcast program as shown in Fig. 3. A query q = < d3, d4, d6 > is requested at the beginning of the `th
cycle. The start-up time TS(q) is 2. After d3is downloaded, d4
and d6are downloaded in the (` + 1)th cycle . In this situation,
the waiting time TW(q) is 0 and TR(q) = 3. Then
TA(q3) = TS(q3) + TW(q3) + TR(q3) = 2 + 0 + 3 = 5. Cycle l TS(q) TA(q) TR(q) TR(q) d1 d2 d3 d1 d2 d3 d4 d5 d6 d4 d6 d5 Cycle l+1 TR(q)
Fig. 3. A broadcast program.
Generally, clients may sent queries in any time or new clients may join in the system spontaneously. The server can not know the access probability of queries when the system is initialized. So the broadcast program needs to be updated when some new queries are sent by clients. Assume that the server updates the broadcast program if necessary and the server uses the new broadcast program for the next broadcast cycle.
III. SCHEDULING
In this section, we will first study the case that the query distribution is known, then extend to the case that the query distribution is unknown.
A. The case that the query distribution is known
If the query distribution is known, the server first sorts it according to the access probability. Then we have the access probability of data items as shown in Table III. Since the server knows all access probability of queries, the average access time of all query TA(Q) can be computed by
TA(Q) = M X i=1 fqi· TA(qi). TABLE III AQUERY DISTRIBUTION. Probability Query Contents
0.3679 q1 < d7, d11, d5, d1, d10> 0.1839 q2 < d1, d12, d3, d10, d7> 0.1226 q3 < d12, d2, d5, d3, d6, d2> 0.0919 q4 < d8, d6, d12, d3, d9> 0.0735 q5 < d9, d8, d3, d10> 0.0613 q6 < d1, d3, d4, d7, d6> 0.0525 q7 < d2, d6, d12, d11> 0.0459 q8 < d11, d8, d3, d10, d4>
Instead of evaluating possible combinations pair by pair, we just check a pair of consecutive data items and the relations of all scheduled queries, then adjust them one by one into some free placements for reducing the average access time for all scheduled queries. Since the channel of data item does not affect the access time, the number of free placements that we check is always less then L. Thus the computation complexity is much lower than that of MULS. The proposed algorithm is described as follows.
Algorithm 1 schedule1
Require: Q: a query set with M = |Q| D: a data item set with N = |D| K: the number of channels
A: the corresponding probability matrix Ensure: The broadcast program matrix P
1. Sort Q according to the access probability in decreasing order.
2. L = dN/Ke
3. P is a K × L matrix
4. for i = 1 to M do
5. for j = 1 to nqi do
6. if qi(j) is unscheduled and qi(j + 1) is unscheduled
then
7. insertAfter(qi(j), L, P )
8. end if
9. if qi(j) is scheduled and qi(j + 1) is unscheduled
then
10. check(qi(j), P )
11. insertAfter(qi(j + 1), L(qi(j)), P )
12. else if qi(j) is unscheduled and qi(j +1) is scheduled
then
13. check(qi(j + 1), P )
14. insertBefore(qi(j), L(qi(j + 1)), P )
15. else if qi(j) is scheduled and qi(j + 1) is scheduled
then 16. check(qi(j), P ) 17. check(qi(j + 1), P ) 18. end if 19. end for 20. end for 21. return P
A[di][dj] represents the access probability of the case di is
requested just before djis requested. The queries are processed
according to the access probability in decreasing order and for each query qiis evaluated by two consecutive items qi(j) and
qi(j + 1) at each stage, 1 ≤ j ≤ nqi− 1. When one of the
two items is scheduled, our algorithm will re-check if there still exists better position for it in this moment. The procedure insertAfter(d, i, P ) allocates the unscheduled data item d to the placement that has the minimum ∆ from position i to d. Likewise, the procedure insertBefore(d, i, P ) allocates the unscheduled data item d to the position with minimum ∆ from d to placement i. The procedure check(d, P ) exchanges d to some free position. The procedure evaluate(d, i) calculates the total access time when d is in the position i.
Figure 5. Example of scheduling. 1 2 3 4 1 1d 7 2d11 3d5 4d1 2 5d 10 7d3 3 6d 12 (a) K 1 2 3 4 1 d7 d11 d5 d1 2 d10 9d12 8d3 3 11d 6 10d2 (b) K 1 2 3 4 1 d7 d11 d5 d1 2 d10 12d6 d12 d3 3 13d 8 14d9 d2 (c) K L 1 2 3 4 1 d7 d11 d5 d1 2 d10 d6 d12 d3 3 16d4 d9 15d8 d2 (d) K L L L
Fig. 4. An example of scheduling.
Consider the example of eight queries as shown in Table III. Assume that the number of channels K is 3. Since there are 12 data items, the length of broadcast cycle L = 12/3 = 4. A is an N × N probability matrix. The element A[di][dj]
records the probability of the case that di requested before
dj. For example, the consecutive items d7 and d11 only are
needed in q1, then A[7][11] = 0.3679. On the other hand,
two consecutive items d12 and d3 are needed in q2 and q4,
A[12][3] = 0.1839 + 0.0919 = 0.2758. Thus we allocate q1 and q2 as shown in Fig. 4(a). When we consider d3 and
d10 in query q2, check(d3, P ) finds better placement for d3
and exchanges it. Similarly, query q3 is arranged as shown
in Fig.4(b) after the steps of d12 and d2. Then query q3 is
adjusted as shown in Fig.4(c) after the steps of d6 and d2.
When d4 is allocated in P , all data items are scheduled as
shown in Fig. 4(d) and the algorithm stops. B. The case that the query distribution is unknown
In real applications, the exact query distribution is hard to obtain because the clients may sent queries or new clients might join in the system in any time. The probability matrix can not be known in advance, so we apply a frequency matrix, denoted by F , to record the history of data items in queries. When the sever receives a new query, it updates the element F [di][dj] by adding 1 after a broadcast cycle is finished, and
then the server re-schedules and uses new broadcast program
in the next broadcast cycle. The related algorithm is described in Algorithm 2.
Algorithm 2 schedule2
Require: Q: a query set with M = |Q| qi: a new unscheduled query
D: a data item set
K: the number of channels
L: the number of positions in each channel F : the corresponding frequency matrix Ensure: The broadcast program matrix P
1. add qi into the unscheduled query set Q 2. for k = 1 to ni do 3. F [qi(k)][qi(k + 1)] = F [qi(k)][qi(k + 1)] + 1 4. if qi(k) /∈ D then 5. add qi(k) into D 6. end if 7. end for 8. N = |D| 9. resize(N, K, L, P ) 10. schedule1(Q, D, K, F ) 11. return P
Since the queries are not static, the size of broadcast program P is not constant. Thus we need to adjust the size of P . If we set L as large as possible, it will take too much time to check free placements for locating a better solution. On the other hand, if L is too small, there are fewer free placements to examine such that the access time will increase. The resize procedure is suggested in Algorithm 3 to alter the dimension of P dynamically for containing some more free placements such that data items can be re-allocated. When the free placements are not enough, K and L are added by 1 simultaneously. Thus, when the systems opens a new channel to schedule, every position in this channel is available to be assigned.
Algorithm 3 resize(N, K, L, P )
Require: N : the number of scheduled items K: the number of channels
L: the number of positions in each channel P : the old broadcast program matrix Ensure: The new broadcast program matrix P
1. while K ∗ L ≤ N + (the average length of queries)/2 do
2. L + + 3. K + + 4. if L > maxL then 5. L = maxL 6. end if 7. if K > maxK then 8. K = maxK 9. end if 10. end while 11. P is a K × L matrix 12. return P
IV. SIMULATION
This section presents the experimental results of schedule1 and schedule2. Two measurements are considered: access time and execution time. The test sample of ordered queries are generated by Zipf distribution [27], fi = (1/i)θ/P
N
j=1(1/j)θ where 1 ≤ i ≤ M and θ
is skewness parameter. When θ = 0, the distribution is uniformly distribution. When θ = 1, the top 20 percent of queries request 80 percent of data items. In busy web sites, the traffic obeys the distribution when θ is large than 1 [22]. A. The case that query distribution is known
The related parameters when the query distribution is known are listed in Table IV. The results are also compared to OLS and MULS [11]. Fig. 5 and Fig. 6 show that schedule1 the average access time is lowest while the execution time is between those of OLS and MULS. This reveals that schedule1takes reasonable amount of time to improve the access time. In fact, MULS may suffer the local minimum problem since it just checks and exchanges possible solutions pair by pair. From Fig. 7, we obtain that the average access time decreases when θ increases. This is because these algo-rithms allocate the higher probability queries first. Moreover the average access time of schedule1 is very close to that of MULS, and it is lowest when θ is large than 0.8.
TABLE IV
PARAMETERS USED WHEN THE QUERY DISTRIBUTION IS KNOWN. Parameters Value Range
N 240 220 ∼ 380
K 12 4 ∼ 12
M 100 100
θ 1.0 0.0 ∼ 1.2
average query length 100 10 ∼ 120
700 750 800 850 900 950 1000 1050 1100 1150 1200 220 240 260 280 300 320 340 360 380 A verage Acc ess T im e (u ni t tim e) N OLS schedule1 MULS
Fig. 5. Average access time with N varied when the query distribution is known.
B. The case that the query distribution is unknown
Table V lists the values of all parameters used when the query distribution is unknown. Since MULS needs more exe-cution time, we just modified the original OLS to be applied in this scenario. From Fig. 8, it is shown that the average access
1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08 220 240 260 280 300 320 340 360 380 Execu ti o n T ime (ms) N OLS schedule1 MULS
Fig. 6. Execution time with N varied when the query distribution is known.
800 900 1000 1100 1200 1300 0 0.2 0.4 0.6 0.8 1 1.2 A verage Acc ess T im e (u ni t tim e) θ OLS schedule1 MULS
Fig. 7. Average access time with θ varied when the query distribution is known.
time increases when N increases and schedule2 algorithm is more efficient than the modified OLS version. Similarly, even to the execution time, schedule2 takes reasonable amount of time to improve the access time.
TABLE V
PARAMETERS USED WHEN THE QUERY DISTRIBUTION IS UNKNOWN. Parameters Value Range
N 200 100 ∼ 400
K 10 10
M 50 50
θ 1.0 0.0 ∼ 1.2
average query length 100 10 query rate per unit time 10 10
V. CONCLUSION
Data broadcasting is an efficient and scalable method to disseminate information to a large amount of mobile clients. In this paper, we studied the problem of data allocation for ordered queries on multiple broadcast channels and proposed an efficient algorithm based on a local search strategy. The experimental results show that our algorithm outperforms the existing algorithms when the query distribution is known. Moreover, our algorithm can be applied efficiently when the query distribution is unknown, and can reduce the average access time as well.
26 28 30 32 34 36 38 40 42 44 46 48 100 150 200 250 300 350 400 A verage Acc ess T im e (u ni t time ) N schedule2 OLS2
Fig. 8. The average access time with N varied when the query distribution is unknown.
REFERENCES
[1] S. Acharya, R. Alonso, M. Franklin and S. Zdonik, ”Broadcast disks: Data management for asymmetric communication environments,” Pro-ceedings of the ACM SIGMOD Conference, 1995, pp. 199-210. [2] S. Acharya, M. Franklin and S. Zdonik, ”Disseminating updates on
broadcast disks,” Proceedings of the 22th International Conference on Very Large Data Bases, 1996, pp. 354-365.
[3] S. Acharya, M. Franklin and S. Zdonik, ”Balancing push and pull for data broadcast,” Proceedings of the 1997 ACM SIGMOD international conference on Management of data, vol. 26, no. 2, 1997, pp. 183-194. [4] Y.C. Chehadeh, A.R. Hurson and M. Kavehrad, ”Object organization on a single broadcast channel in the mobile computing environment,” Multimedia Tools and Applications, vol. 9, no. 1, 1999, pp. 69-94. [5] Y.D. Chung and M.H. Kim, ”QEM: A scheduling method for wireless
broadcast data,” Proceedings of the Sixth International Conference on Database Systems for Advanced Applications, 1999, pp. 135-142. [6] Y.D. Chung and M.H. Kim, ”Effective data placement for wireless
broadcast,” Distributed and Parallel Databases, vol. 9, no. 2, 2001, pp. 133-150.
[7] S.M.S. Google, ”Google Short Message Service(SMS),” 2005; http://www.google.com/sms/.
[8] J.L. Huang and M.S. Chen, ”Dependent data broadcasting for unordered queries in a multiple channel mobile environment,” IEEE Transactions on Knowledge and Data Engineering,vol. 16, no. 9, 2004, pp. 1143-1156.
[9] J.L. Huang and M.S. Chen, ”Exploiting replication on dependent data al-location for ordered queries over multiple broadcast channels,” Wireless Networks, published online.
[10] J.L. Huang, M.S. Chen and W.C. Peng, ”Broadcasting dependent data for ordered queries without replication in a multi-channel mobile envi-ronment,” Proceedings - International Conference on Data Engineering, 2003, pp. 692-694.
[11] H.P. Hung and M.S. Chen, ”MULS: A general framework of providing multilevel service quality in sequential data broadcasting,” IEEE Trans-actions on Knowledge and Data Engineering, vol. 19, no. 10, 2007, pp. 1433-1447.
[12] H.P. Hung, J.W. Huang, J.L. Huang and M.S. Chen, ”Scheduling dependent items in data broadcasting environments,” Proceedings of the 2006 ACM symposium on Applied computing, 2006.
[13] G. Lee and S.C. Lo, ”Broadcast data allocation for efficient access of multiple data items in mobile environments,” Mobile Networks and Applications, vol. 8, no. 4, 2003, pp. 365-375.
[14] G. Lee, S.C. Lo and A.L.P. Chen, ”Data allocation on wireless broadcast channels for efficient query processing,” IEEE Transactions on Comput-ers, vol. 51, no. 10, 2002, pp. 1237-1252.
[15] K.C.K. Lee, W.C. Lee and S. Madria, ”Pervasive data access in wireless and mobile computing environments,” Wireless Communications and Mobile Computing, vol. 8, no. 1, 2008, pp. 25-44.
[16] H.V. Leong and A. Si, ”Data broadcasting strategies over multiple unreliable wireless channels,” International Conference on Information and Knowledge Management, Proceedings, 1995, pp. 96-104.
[17] K.F. Lin and C.M. Liu, ”Broadcasting dependent data with minimized access latency in a multi-channel environment,” IWCMC 2006 - Pro-ceedings of the 2006 International Wireless Communications and Mobile Computing Conference, pp. 809-814.
[18] K.F. Lin and C.M. Liu, ”Schedules with minimized access latency for disseminating dependent information on multiple channels,” Proceedings -2006 IEEE International Conference on Sensor Networks, Ubiquitous, and Trustworthy Computing, pp. 344-351.
[19] C.M. Liu and K.F. Lin, ”Efficient scheduling algorithms for disseminating dependent data in wireless mobile environments,” Proceedings -2005 IEEE International Conference on Wireless Networks, Communi-cations and Mobile Computing, 2005.
[20] S.C. Lo and A.L.P. Chen, ”Optimal index and data allocation in multiple broadcast channels,” Proceedings - International Conference on Data Engineering, 2000, pp. 293-302.
[21] S.P.O.T. Microsoft, ”Microsoft DirectBand Network,” 2006; http://www.msndirect.com/.
[22] V. Padmanabhan and L. Qiu, ”The content and access dynamics of a busy web site: findings and implications,” Proceedings of the conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, 2000.
[23] W.C. Peng and M.S. Chen, ”Efficient channel allocation tree generation for data broadcasting in a mobile computing environment,” Wireless Networks, vol. 9, no. 2, 2003, pp. 117-129.
[24] K. Prabhakara, K.A. Hua and J. Oh, ”Multi-level multi-channel air cache designs for broadcasting in a mobile environment,” Proceedings - International Conference on Data Engineering, 2000, pp. 167-176. [25] A. Si and H. Va Leong, ”Query optimization for broadcast database,”
Data and Knowledge Engineering, vol. 29, no. 3, 1999, pp. 351-380. [26] K. Stathatos, N. Roussopoulos and J.S. Baras, ”Adaptive data broadcast
in hybrid networks,” Proceedings of the 23rd International Conference on Very Large Data Bases, 1997, pp. 326-335.
[27] G.K. Zipf, Human Behavior and the Principle of Least Effort: An Introduction to Human ecology, Addison-Wesley Press, Cambridge, MA., 1949.
