- Email: [email protected]
Dynamic multi-channel assignment using network flows in wireless data networks
Microprocessors and Microsystems 28 (2004) 417–426 www.elsevier.com/locate/micpro
Dynamic multi-channel assignment using network flows in wireless data networks Sajal K. Dasa, Osman Koyuncub,* a
Center for Research in Wireless Mobility and Networking (CReWMaN), Department of Computer Science and Engineering, University of Texas at Arlington, Arlington, TX 76019, USA b High Speed Communications and Control Division, Texas Instruments Inc., 12500 TI Boulevard MS 8675, Dallas, TX 75243, USA Received 11 December 2003; revised 31 December 2003; accepted 20 February 2004 Available online 12 March 2004
Abstract The radio frequency spectrum, a scarce resource in mobile communications, has to be efficiently utilized with the objectives of increasing the network capacity and minimizing the interference. A variety of channel assignment strategies have been developed to achieve these objectives. As the cell sizes get smaller, there is a greater need for efficient channel assignment algorithms which are desired to dynamically balance the load of the system. We propose a dynamic multi-channel assignment (DMCA) algorithm where the assignment decision is assisted by the mobiles. Our algorithm is based on the concept of network flows and handles all the events in the system gracefully. Several existing channel assignment algorithms can be easily modeled in the proposed network flow framework model. Simulation results show that DMCA algorithm performs well under heavy traffic conditions and handles different traffic classes gracefully. q 2004 Elsevier B.V. All rights reserved. Keywords: Dynamic channel assignment; Flow network
1. Introduction The growing demand for mobile communications and portable computing devices coupled with the limited allowed radio frequency spectrum for this use, led to the problem of efficient management of resources like bandwidth in wireless networks. Thus evolved the concept of a cellular architecture, in which frequency can be reused in cells at a safe distance apart so as to guarantee no or minimal interference among the cells involved. Existing cellular systems generally use some variations of a fixed channel assignment (FCA) scheme in which a cell is assigned a fixed subset of the available channels [3]. The main drawback of such an assignment is that the system cannot adapt to changes in the channel demands of the user traffic. In some variants of the FCA scheme, a cell can borrow channels from its neighbors to satisfy the additional requests. Also, channels can be migrated from cells which are not necessarily the neighbors of the needy cell [2]. In another * Corresponding author. Tel.: þ 1-214-480-0685; fax: þ1-214-480-3555. E-mail addresses: [email protected] (O. Koyuncu), das@cse. uta.edu (S.K. Das). 0141-9331/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.micpro.2004.02.004
class of schemes, called the dynamic channel assignment (DCA) schemes, all the channels are available for assignment to every cell but the usage of these channels is constrained by the interference experienced. Since the reuse of channels is time-varying, the system dynamically attempts to minimize the mutual interference among all active channels [4]. Although the DCA strategies are more flexible and increase the utilization of the channels, yet the high cost of managing the channel allocation and maintenance of interference information becomes a critical issue. For different algorithms on DCA, refer to Ref. [7]. This paper extends the network flow framework proposed in Refs. [8,9], to design dynamic multi-channel assignment (DMCA) algorithm for supporting wireless multimedia services. The proposed on-line algorithm dynamically assigns channels to users upon demand, and also reassigns channels among users when the interference degrades below a threshold. The assignment decision of a number of channels to a new call is made locally which may possibly involve reassignment of a certain number of active calls to other channels. Reconfiguration is also necessary when a mobile has to be reassigned to a better quality
418
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
channel (which experiences less interference), if possible. Our algorithm handles reassignments in an incremental manner rather than a global re-computation of assignments. Our results show that DMCA algorithm handles different traffic classes better than FCA and provides good performance under heavy traffic load conditions. This paper is organized as follows. Section 2 introduces the network flow framework and the construction of a flow network for DMCA. Section 3 presents the algorithm and explains how the multi-channel assignment, call termination and handoff are handled. This section also presents how the DMCA algorithm attempts to maintain the quality of service for different traffic classes. In Section 4, other channel assignment schemes and their relation to the network flow framework are discussed. Section 5 describes the simulation environment and the experiments performed. Conclusions are given in Section 6. An explanation of the signal propagation model used in the simulations is presented in Appendix.
2. Network flow framework This section first introduces flow networks and the related terminology. (For details, refer to Ref. [1].) Then we model the DMCA problem with the help of flow networks. Definition 1. A flow network, GF ¼ ðV; EÞ; is a directed graph in which the vertex set V contains two designated vertices, s for the source and t for the sink. Each edge in the set E has non-negative upper ðuÞ and lower ðlÞ capacity limits. A cost ðcÞ is also associated with each edge in the network. Definition 2. A flow f in GF is a real function f : V £ V ! R such that the net flow f ðv; wÞ satisfies the following properties: † lðv; wÞ # f ðv; wÞ # uðv; wÞ and f ðv; wÞ ¼ 2f ðw; vÞ for v; w P[ V † v[V f ðv; wÞ ¼ 0 for w [ V 2 {s; t} The residual capacity of an edge ðv; wÞ; denoted as rf ðv; wÞ is given by uðv; wÞ 2 f ðv; wÞ: Given a flow network GF ¼ ðV; EÞ and a flow f ; the residual network of GF is a graph composed of only edges with positive residual capacities. 2.1. Modeling DCA problem Let N denote the number of base stations in the network coverage area where a base station, Bk ; has the capacity to support ck channels. The following sets of vertices and edges are defined: † Vb ¼ {B1 ; B2 ; …; BN } is the set of vertices corresponding to the base stations,
† Vch ¼ {ch11 ; ch12 ; …; chCN N } is the set of vertices where chjk corresponds to channel1 j being supported under base station Bk ; † Vm ¼ {m1 ; m2 ; …} is the set of vertices corresponding to active mobiles in the system, † E1 ¼ {ðs; mi Þlmi [ Vm }; E2 ¼ {ðmi ; chjk Þ} such that mobile mi can potentially use channel chjk ; E3 ¼ {ðchjk ; Bk Þlchjk [ Vch ; Bk [ Vb }; E4 ¼ {ðBk ; tÞlBk [ Vb } Let there be K classes of multimedia services supported by the network where a call of class k ð1 # k # KÞ initiated by mobile mi ; requires minimum of lki and a maximum of uki channels. We construct the flow network, GF ¼ ðV; EÞ; for DMCA, such that V ¼ {Vm < Vb < Vch < {s; t}} and E ¼ {E1 < E2 < E3 < E4 }: The terms ‘mobile’, ‘base station’ and ‘channel’ will be used to also refer to the corresponding vertices in the flow network. Given the set of edges and vertices as above, assignment of lower, upper capacity and cost values to edges is done as follows. Cost(c): For edges from the source ðsÞ to mobiles and base stations to the sink ðtÞ; the cost is set to zero. For edges from the mobiles to channels, the cost is set to the inverse of the carrier to interference ratio (CIR), that the mobile will experience when using the corresponding channel (denoted by Rmi ðv; wÞ). This interference is caused by down-link transmissions of other base stations that use the same channel while the carrier strength is the received signal strength from the candidate base station, (see Appendix for signal propagation and interference calculations). For edges from the channels to base stations, the cost is set to the interference level that the base station will experience when using the corresponding channel (denoted by RBk ðv; wÞ). This interference is caused by up-link transmissions of other mobile users that use the same channel. Upper Capacity(u): For edges from the base stations to the sink, the upper capacity is set to the respective number of channels supported under each base station. For edges from mobiles to channels and from channels to base stations, it is set to 1. For edges from the source to mobiles, the upper capacity is set to the maximum number of channels required by the respective mobile for its service class. Lower Capacity(l): For edges from base stations to the sink, from mobiles to channels and from channels to base stations, the lower capacity is set to zero. For edges from the source to mobiles, it is set to the minimum number of channels required by the respective mobile for its service class. Example 1. Fig. 1 illustrates a flow network corresponding to base stations (B1 and B2 ), each supporting three channels. We assume that there are active mobiles under 1 A channel in our framework consists of an up-link and a down-link portion which are predetermined pairs.
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
419
Fig. 1. Flow network example.
neighboring base stations but there is currently one mobile user which just became active under base station B1 and there is no active mobile under base station B2 : The corresponding flow network also implies that the mobile m1 can potentially use channel ch11, ch21 or ch31. The triplet of values associated with each edge of this network corresponds to the l; u; and c values of that edge. In this flow network, one unit of flow pushed from the source to the sink corresponds to an assignment of a particular mobile to a channel under a base station. In other words, at any instance of time, a maximum possible flow from s to t (max-flow) induces a set of assignments where each element of this assignment is a triplet of (mobile, channel, base station). Given an instance of GF ; we can employ a max-flow algorithm to find the assignment set whose cardinality is maximum.
the mobile will communicate with; the set of channels, Vch ; that can potentially be used by the mobile and their corresponding interference levels, Rmi : Next the flow network is expanded by adding edges from the mobile node mi to the nodes corresponding to the candidate channels in Vch : While doing so, no edge is added to the channels for which the interference level is above a threshold value. For each edge added to the flow network, its cost is assigned as the corresponding interference level in Rmi : Then we attempt to find as many minimum-cost augmenting paths from the source to the sink as the minimum number of channels, lki ; required by the mobile such that the augmenting paths include the new mobile. This requires finding lki many shortest paths from s to t that goes through mi : If we can not find lki many paths, the new call is blocked since the base station can not provide enough channels for the mobile to start its communication. Fig. 2 illustrates the flow chart for the algorithm. In call admission
3. Dynamic multi-channel assignment algorithm (DMCA) In this section, we explain our system model and how to utilize flow networks for DMCA. We describe in details the two-stage algorithm for DMCA. Each base station controller (BSC) in the system constructs a flow network GF ¼ ðV; EÞ as explained in Section 2. The channel assignment algorithm then proceeds with different trigger events being handled differently. 3.1. DMCA-first stage When a new call arrives, it has to be admitted by incurring as little cost as possible. In our case, the cost is the experienced interference by the communicating parties. The algorithm starts with expanding the flow network GF such that a new vertex is created for the new mobile. Let mi be the new mobile that requests service from the system. At the time of a call arrival, the BSC knows which base station, Bk ;
Fig. 2. Flowchart for DMCA-first stage.
420
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
Fig. 3. Actual flow after DMCA-first stage.
attempt, the algorithm does not perform a global computation on the flow network that would slow down the response time dramatically. Instead, it performs a local augmentation of the flow to find a channel that can be assigned to the new mobile. Furthermore, an upper threshold ðLÞ on the path length can be set to prevent the shortest path algorithm considering long paths that would cause reassignment of several other mobiles to other channels or base stations. Fig. 3 illustrates the actual flow from the source to the sink after the execution of the first stage of the algorithm on the flow network of Example 1 (since base station B2 is not involved in our running example it is not shown in the rest of the figures). This flow structure corresponds to the assignment of the channels ch11 and ch31 to the mobile m1 under base station B1 : Fig. 4 illustrates the structure of the corresponding residual network. In this residual network, the backward edges (dark-colored edges) appear which are not a part of the original flow network. These edges represent the potential for pushing back (canceling) the existing flow in the network. Costs of such edges are negative since canceling an existing flow would also eliminate the associated cost. As will be explained later, canceling one unit of flow would correspond to a reassignment of a channel, since the cancelled flow would be re-routed to another channel and/or a base station. Based on the assignment outcome for our example, mobile m1 is assigned to the maximum number of channels that it requested (m1 has requested a minimum of one and a maximum of two channels). This implies that the system should be able to reassign one of m1 ’s channels if and when it is required by other mobiles under heavy traffic load. In other words, the channel assignment algorithm should be capable of degrading m1 ’s service for the sake of admitting
other mobiles to the system. This is addressed by the second stage of the algorithm. 3.2. DMCA-second stage Once the incoming call is accepted, we perform the second stage of the DMCA algorithm. The purpose of this stage is to modify the structure of the residual network to enable the degradation or improvement of the assignment for the newly accepted mobile mi and to modify the cost structure to include the reassignment penalties. To enable the degradation of the assignment of mobile mi ; we create a (redundant) vertex di associated with mi and add the following edges to the residual network. An edge ðmi ; di Þ with a lower capacity of l ¼ 0; an upper capacity of u ¼ f ðs; mi Þ 2 lik and a cost c ¼ cmax þ 1 where cmax is the maximum possible edge cost in the graph. We also add an edge ðdi ; tÞ with l ¼ u ¼ c ¼ 0: In order to incorporate the cost of reassignments, we add the value of ak to the cost of the backward edges ðchjk ; mi Þ in the residual network (that have non-zero flow in the flow network). The intuition behind this is that, in order to reassign a channel chjk from mobile mi to another mobile ml ; the new mobile ml has to have at least ak units less than the interference level of mi : This is the penalty that has to be paid for a reassignment. Fig. 5 illustrates the residual network for Example 1 after the above transformation with ak ¼ 3: Intuitively, f ðs; mi Þ represents the number of channels currently assigned to a mobile mi and ðf ðs; mi Þ 2 lik Þ is the number of channels that mi may be forced to sacrifice by the BSC to accommodate other users. However, due to the way the upper capacity bound is assigned, the mobile can not be forced to give up channels so that it occupies less than its minimum bandwidth requirements. The cost assignment of c ¼ cmax þ 1 to
Fig. 4. Residual network after DMCA-first stage.
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
421
Fig. 5. Residual network after DMCA second stage.
the edge di prevents unnecessary degradation of mi ’s assignment while there are other channels available.
and the flow values are updated as follows: † Delete edges ðs; mi Þ and ðmi ; chjk Þ:
Example 2. In Fig. 6 another mobile m2 just became active and requests channels from the system. Also m2 requires exactly two channels for its service class (for clarity only edge costs and relevant channels are shown in the figure). The first stage of the DMCA algorithm will find the first path P1 as ks; m2 ; ch11 ; B1 ; tl with a total cost of 30, and the second path P2 as ks; m2 ; ch11 ; m1 ; d1 ; tl with a total cost of ð37 2 12 þ cmax þ 1 ¼ cmax þ 26Þ: The other candidate path ks; m2 ; ch31 ; m1 ; d1 ; tl has a cost of ð27 2 1 þ cmax þ 1 ¼ cmax þ 27Þ which eliminates it from being the second shortest path. Pushing one unit of flow through P2 will reassign ch11 from mobile m1 to mobile m2 : While satisfying the minimum channel demand of m2 ; this reassignment downgrades the assignment of m1 by one channel. This reassignment is reflected in the residual network of Fig. 7.
3.3. Call termination On termination of mobile mi ’s call, the corresponding vertex and adjacent edges for that mobile are deleted
† Decrement flow value of all edges (chlk ; Bk ) where chlk is the channel mi was using. For each such channel, decrement the flow value of the edge (Bk ; t:) 3.4. Reassignment (handoff) Whenever a mobile mi ; who is using channel chjk ; begins to experience an intolerable interference, it notifies the BSC and the system has to reassign mi to another channel (possibly under another base station). At this point, the BSC updates the network by deleting the edge ðmi ; chjk Þ and then executing a shortest path algorithm to find another augmenting path. If such a path exists, the mobile is reassigned to the corresponding channel on the path. Otherwise, if loosing chjk decrements the number of channels to below lik ; the ongoing call is dropped. This first type of reassignment is mobile-assisted and triggered by the fact that the mobile is experiencing high interference. When a mobile notifies a BSC of high interference, it also provides a list of channels that it can potentially use and a base station id which it receives the strongest signal from.
Fig. 6. Residual network after mobile m2 arrived.
422
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
Fig. 7. Residual network after mobile m2 is accepted.
The second type of reassignments is initiated by the base station based on the interference experienced on the uplink channel. When the ratio RB of received interference to carrier strength is above a threshold over a particular channel, it triggers a reassignment in which case the BSC removes the edge from the channel to the requesting base station and runs a shortest path algorithm on the residual network from the mobile which was using the channel. If it finds a path that goes through the initiating base station, it augments the flow accordingly in which case the uplink channel is handed off gracefully. Otherwise, loosing the uplink channel may degrade the bandwidth or cause a call drop. Reassignments that are initiated by the mobiles or the base stations can be either within the same cell (intra-cell reassignment) or between two neighboring cells (inter-cell reassignments). Intra-cell reassignments incur a penalty of a into the overall cost and this penalty can be used to control the reassignments in the system. Similarly, inter-cell reassignments incur a penalty of b: These parameters are system-wide and facilitate the fine tuning of the reassignment rates.
corresponding base station and when borrowing occurs the BSC removes the incoming edge to the donor base station (and all other cells that needs to be prohibited), re-creates it for the borrowing base station. This mechanism explicitly locks the borrowed channel. 4.2. Distributed channel assignment schemes ([5,12,13]) When the flow network is constructed per base station, the distributed algorithms are easily modeled. Each base station constructs flow network for its supported channels. Since the cost function is based on the Rm and RB values and interference measurements are done independently by each base station and mobile, the cost assignments are as explained before. The inter-cell handoffs are handled by the BSC. 4.3. DCA schemes ([5,7,10,11]) The main idea of all DCA schemes is to evaluate the cost of using each candidate channel, and select the one with the minimum cost provided that certain interference constraints are satisfied. The selection of the cost function is what
4. Network flow framework and existing algorithms One attractive feature of the proposed network flow framework is that it is able to model several different variants of the channel assignment algorithms reported in the literature. In this section we will present some examples of how this model captures several properties of other algorithms. 4.1. Channel borrowing schemes for FCA ([2,14,15]) In a channel borrowing scheme, a base station that has used all its assigned channels can borrow free channels from its neighboring cells. Several other cells are prohibited from using the borrowed channel by locking the channel in those cells. This is to ensure avoidance of channel interference. Creating the flow network for FCA with channel borrowing requires that each channel has an edge to its
Fig. 8. Base station layout.
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426 Table 1 Network services used in simulations Traffic class
Channels required
Calls (%)
Average connection time
Example
1 2 3 4 5
1 5–10 1–10 8–25 5–15
75 5 10 3 5
1.5 min 5 min 30 s 10 min 3 min
Voice services Video phone/conferencing E-mail, paging, fax Interactive multimedia File transfer, remote login
differentiates DCA schemes from each other. Our proposed algorithm is based on the interference measurement. However, the network flow model handles the call arrivals and handovers gracefully independent of what the cost function is. One example of such cost functions is the future blocking probability in the vicinity of the cell in which the call is initiated [10,11]. In our framework, based on the history of the system, the BSC can assign more cost to the edges to/ from nodes corresponding to such channels that caused high call blocking in the vicinity. 4.4. Deadlock and instability prevention Existing algorithms (so is the one presented in this paper) that employ the interference measurement and adaptation schemes may suffer from instability in which an assignment decision made locally can have ripple affect by increasing the interference experienced by several ongoing calls in the neighboring cells. An accepted call in one cell may trigger reassignments in several other cells and the overall system may never converge to a stable state. Although the algorithm presented in this paper guarantees that a newly accepted call would not reduce the number of channels that are already acquired by other mobiles below their lower bound, it does not predict the system-wide effect and does not predict the interference effect on the acquired channel in the neighboring cells.
423
However, as stated earlier, in our network flow model, assignment or reassignment of certain channels can be discouraged by selectively assigning higher costs to edges incident to those channels. The trade-off between avoiding call blocking and avoiding service interruptions (call drops) can be fine tuned and reflected in the model. One such algorithm is to limit the number of reassignments that would be incurred when trying to accept a new mobile into the network. By varying the number of acceptable reassignments (this can be achieved by limiting the number of mobile nodes visited in the shortest augmenting path algorithm), the system performance can be fine-tuned.
5. Simulation results We have simulated our DMCA algorithm over a real cellular network with coverage area of 54 base stations that represents an actual metropolitan area (Fig. 8). Traffic data is based on collected busy-hour call attempts in the coverage area. The following parameters are used in the simulation: † † † † † †
Call arrival rate Call holding time Minimum acceptable C/I ratio Intra-cell reassignment penalty ðaÞ; Inter-cell reassignment penalty ðbÞ; Number of channels supported in each base station.
In order to represent different multimedia applications, five different traffic classes are assumed based on the connection duration and bandwidth requirement (Table 1). These are typical applications seen on existing networks. Call arrival and handoff rates are driven from the collected traffic data which represented 52,000 calls/h. Figs. 9 and 10 illustrate the blocking/dropping probabilities for each traffic class under non-uniform traffic patterns for limited and unlimited number of reassignment thresholds, respectively. As explained before, setting
Fig. 9. Number of handoffs limited to 3.
424
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
Fig. 10. Unlimited number of handoffs.
a limit on the number of inter/intra-cell reassignments prevents a system-wide instability but also as seen in the charts, compromises the blocking probability. As expected, this reassignment limit does not have as much impact on the call drop rate as the blocking rate. Lower bandwidth service classes, however, are impacted by the limit more than the higher bandwidth service classes. This same effect is not observed when we set no limit on the reassignments but assign higher reassignment penalties. In the latter case, when an augmenting shortest path is to be found, the algorithm performs the reassignment even though the total cost of the path is higher (since it is still a path from the source to the sink no matter how costly it is). We have also experimented on limiting the number of channels that a higher bandwidth class mobile can acquire (between its min and max range) when it is first accepted into the network. This did not have noticeable performance impact on the system other than a negligible improvement on the drop rate. Another observation is that, services that require higher bandwidth have higher blocking probability but once they are admitted into the system, the algorithm attempts to keep the assigned channels (potentially blocking other calls); that is why these traffic classes have less dropping probability compared to their blocking probability. Figs. 11 and 12 illustrate the performance of the algorithm in comparison with FCA under non-uniform
and uniform traffic patterns. For non-uniform traffic pattern, the traffic intensity over each cell is determined randomly. For FCA algorithm, the frequency reuse pattern that determines the cluster of cells that a channel can not be reused (see Ref. [3] for details). Another set of experiments is done on the call setup time performance of the DMCA. Call setup time is the time it takes for the system to establish the connection for the call (in our case assign required number of channels) from the time the call has arrived. The comparison to the call setup time of FCA with a reuse factor of 7 (denoted by GFCA ) is illustrated in Fig. 13. As expected, the DMCA takes longer to establish the call as compared to the FCA, since the decision in FCA is straightforward. Also if the number of reassignments are not limited, as the load is increased, the DMCA call setup performance degrades whereas when the reassignments are limited, the call setup time stabilizes. Call setup time performance of the DMCA is a tradeoff between increased capacity versus the response time.
Fig. 11. Performance under non-uniform load.
Fig. 12. Performance under uniform load.
6. Conclusion In this paper, we presented a network flow based framework and an algorithm for DMCA which uniformly handles different types of traffic classes requiring different number of channels. In particular, upper and lower capacity
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
425
loss for received power and interference calculations. The CIR for a mobile, mi ; is defined as
C ðB Þ Rm i ¼ X r C Cr ðBt Þ t[IB
where, Cr ðBÞ is the received signal power (dBm) from base station B as measured by the mobile mi ; BC is the candidate base station, and IB is the set of interfering base stations. For the candidate base station:
Fig. 13. FCA-to-DMCA call setup time ratio ðGFCA =GDMCA Þ:
limits in the flow network captures the minimum and maximum number of channels required by different types of traffic classes. This framework not only captures several fundamental aspects of wireless mobile networks and handles the channel assignment related events in the system gracefully but also uses a realistic cost model. It also has several parameters that can be fine-tuned to improve different performance objectives. The algorithm presented, makes the assignment decision through local computations on the flow graph rather than global reorganization of the existing assignment. Instead of running a min-cost max-flow algorithm from scratch, the algorithm runs a shortest path algorithm from source node to the sink whose locality can be fine tuned by limiting the number of reassignments. The number of intra- and inter-cell reassignments can easily be limited to a desired threshold (due to the layered structure of the flow network) to prevent reassignments leading to instability in the network. Our model supports multiple traffic classes and suitable for multi-service networks. The degradation and upgrade of an existing calls for active mobiles within their respective traffic class limits are handled seamlessly and can be easily adapted to distributed systems.
Appendix A Computation of signal propagation parameters is an important part of the simulation since our channel assignment algorithm uses the CIR ratios experienced by the candidate mobile and the candidate base station in determining the edge costs in the flow network. For this purpose, it is necessary to calculate predicted values of received power (signal strength) at a particular distance. The candidate mobile will experience interference due to the co-channel base stations of its own candidate base station. Similarly, the candidate base station will experience interference from the mobiles in the neighboring base stations that use the same frequency as the candidate mobile. In our model we assumed a dense urban area path
C ðm Þ RB C ¼ X r i Cr ðmj Þ j[Im
where, Cr ðmÞ is the received signal power (dBm) from mobile m as measured by the base station Bc ; mi is the candidate mobile and Im is the set of interfering mobiles. We have used an 8 dB log-normal standard deviation over the mean power values [3]. In our simulations, we have used ETSI Cost-231 Walfish-Ikegami model for small cells in the range of 200 m to 3 km and COST-231 Hata model in ranges over 3 km [6]. When using these models, we have fixed several parameters for simplicity such as antenna heights, building height assumptions, etc. Although we do not explicitly use terrain data in our simulations, COST-231 models have effects of building heights, width and direction of the roads, multi screen diffraction and scatter loss inherent in them. We only considered the omni-directional base station sites, therefore we do not take advantage of directional antenna interference reduction properties. We assume all the mobiles are of the same power class with the assumed maximum power of 2 W (33 dBm) and all the base stations have maximum power of 20 W (43 dBm).
References [1] L.R. Ford Jr., D.R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, 1962. [2] S.K. Das, S.K. Sen, R. Jayaram, A novel load balancing scheme for the tele-traffic hot spot problem in cellular networks, Wireless Networks (WINET) 4 (4) (1998) 325– 340. [3] W.C.Y. Lee, Mobile Cellular Telecommunications: Analog and Digital Systems, McGraw-Hill, New York, 1995. [4] T.S. Rappaport, Wireless Communications Systems, IEEE Press, New York, 1996. [5] A. Lozano, D.C. Cox, Distributed dynamic channel assignment in TDMA mobile communication systems, IEEE Transactions on Vehicular Technology 51 (6) (2002) 1397– 1406. [6] ETSI Technical report ETR 364, Digital Cellular Communications System: Radio network planning aspects, November 1996. [7] J.C. Chuang, Performance issues and algorithms for dynamic channel assignment, IEEE Journal on Selected Areas in Communication 11 (6) (1993). [8] O. Koyuncu, S.K. Das, H. Ernam, Dynamic resource assignment using network flows in wireless data networks, 49th IEEE Vehicular Technology Conference, vol. 1, 1999, pp. 1–5. [9] O. Koyuncu, S.K. Das, H. Ernam, Design and implementation of a dynamic channel assignment algorithm using network flows, Proceed-
426
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
ings of Second International Workshop on Discrete Algorithms and Methods for Mobility, Dallas, Texas, October 1998. [10] M. Zhang, T.-S. Yum, The non-uniform compact pattern allocation algorithm for cellular mobile systems, IEEE Transactions on Vehicular Techology VT-40 (1991) 387–391. [11] M. Zhang, Comparisons of channel assignment strategies in cellular mobile telephone systems, IEEE Transactions on Vehicular Techology VT-38 (1989) 211 –215. [12] M. Frodigh, Reuse partitioning with traffic adaptive channel assignmentfor highway microcellular radio systems, Proceedings of GLOBECOM (1992) 1414–1418.
[13] C.W. Sung, K.W. Shum, Assignment and layer selection in hierarchical cellular system with fuzzy control, IEEE Transactions on Vehicular Technology 50 (3) (2001) 657–663. [14] V.T. Vakili, A. Aziminejad, A new channel borrowing assignment scheme: teletraffic performance evaluation through discrete event modeling in a mobile cellular environment, Proceedings of the 7th International Conference on Telecommunications, vol. 1, 2003, pp. 279–286. [15] S. Mitra, S. DasBit, A load balancing strategy using dynamic channel assignment and channel borrowing in cellular mobile environment, IEEE International Conference on Personal Wireless Communications, December 2000, pp. 278 –282.
Dynamic multi-channel assignment using network flows in wireless data networks Sajal K. Dasa, Osman Koyuncub,* a
Center for Research in Wireless Mobility and Networking (CReWMaN), Department of Computer Science and Engineering, University of Texas at Arlington, Arlington, TX 76019, USA b High Speed Communications and Control Division, Texas Instruments Inc., 12500 TI Boulevard MS 8675, Dallas, TX 75243, USA Received 11 December 2003; revised 31 December 2003; accepted 20 February 2004 Available online 12 March 2004
Abstract The radio frequency spectrum, a scarce resource in mobile communications, has to be efficiently utilized with the objectives of increasing the network capacity and minimizing the interference. A variety of channel assignment strategies have been developed to achieve these objectives. As the cell sizes get smaller, there is a greater need for efficient channel assignment algorithms which are desired to dynamically balance the load of the system. We propose a dynamic multi-channel assignment (DMCA) algorithm where the assignment decision is assisted by the mobiles. Our algorithm is based on the concept of network flows and handles all the events in the system gracefully. Several existing channel assignment algorithms can be easily modeled in the proposed network flow framework model. Simulation results show that DMCA algorithm performs well under heavy traffic conditions and handles different traffic classes gracefully. q 2004 Elsevier B.V. All rights reserved. Keywords: Dynamic channel assignment; Flow network
1. Introduction The growing demand for mobile communications and portable computing devices coupled with the limited allowed radio frequency spectrum for this use, led to the problem of efficient management of resources like bandwidth in wireless networks. Thus evolved the concept of a cellular architecture, in which frequency can be reused in cells at a safe distance apart so as to guarantee no or minimal interference among the cells involved. Existing cellular systems generally use some variations of a fixed channel assignment (FCA) scheme in which a cell is assigned a fixed subset of the available channels [3]. The main drawback of such an assignment is that the system cannot adapt to changes in the channel demands of the user traffic. In some variants of the FCA scheme, a cell can borrow channels from its neighbors to satisfy the additional requests. Also, channels can be migrated from cells which are not necessarily the neighbors of the needy cell [2]. In another * Corresponding author. Tel.: þ 1-214-480-0685; fax: þ1-214-480-3555. E-mail addresses: [email protected] (O. Koyuncu), das@cse. uta.edu (S.K. Das). 0141-9331/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.micpro.2004.02.004
class of schemes, called the dynamic channel assignment (DCA) schemes, all the channels are available for assignment to every cell but the usage of these channels is constrained by the interference experienced. Since the reuse of channels is time-varying, the system dynamically attempts to minimize the mutual interference among all active channels [4]. Although the DCA strategies are more flexible and increase the utilization of the channels, yet the high cost of managing the channel allocation and maintenance of interference information becomes a critical issue. For different algorithms on DCA, refer to Ref. [7]. This paper extends the network flow framework proposed in Refs. [8,9], to design dynamic multi-channel assignment (DMCA) algorithm for supporting wireless multimedia services. The proposed on-line algorithm dynamically assigns channels to users upon demand, and also reassigns channels among users when the interference degrades below a threshold. The assignment decision of a number of channels to a new call is made locally which may possibly involve reassignment of a certain number of active calls to other channels. Reconfiguration is also necessary when a mobile has to be reassigned to a better quality
418
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
channel (which experiences less interference), if possible. Our algorithm handles reassignments in an incremental manner rather than a global re-computation of assignments. Our results show that DMCA algorithm handles different traffic classes better than FCA and provides good performance under heavy traffic load conditions. This paper is organized as follows. Section 2 introduces the network flow framework and the construction of a flow network for DMCA. Section 3 presents the algorithm and explains how the multi-channel assignment, call termination and handoff are handled. This section also presents how the DMCA algorithm attempts to maintain the quality of service for different traffic classes. In Section 4, other channel assignment schemes and their relation to the network flow framework are discussed. Section 5 describes the simulation environment and the experiments performed. Conclusions are given in Section 6. An explanation of the signal propagation model used in the simulations is presented in Appendix.
2. Network flow framework This section first introduces flow networks and the related terminology. (For details, refer to Ref. [1].) Then we model the DMCA problem with the help of flow networks. Definition 1. A flow network, GF ¼ ðV; EÞ; is a directed graph in which the vertex set V contains two designated vertices, s for the source and t for the sink. Each edge in the set E has non-negative upper ðuÞ and lower ðlÞ capacity limits. A cost ðcÞ is also associated with each edge in the network. Definition 2. A flow f in GF is a real function f : V £ V ! R such that the net flow f ðv; wÞ satisfies the following properties: † lðv; wÞ # f ðv; wÞ # uðv; wÞ and f ðv; wÞ ¼ 2f ðw; vÞ for v; w P[ V † v[V f ðv; wÞ ¼ 0 for w [ V 2 {s; t} The residual capacity of an edge ðv; wÞ; denoted as rf ðv; wÞ is given by uðv; wÞ 2 f ðv; wÞ: Given a flow network GF ¼ ðV; EÞ and a flow f ; the residual network of GF is a graph composed of only edges with positive residual capacities. 2.1. Modeling DCA problem Let N denote the number of base stations in the network coverage area where a base station, Bk ; has the capacity to support ck channels. The following sets of vertices and edges are defined: † Vb ¼ {B1 ; B2 ; …; BN } is the set of vertices corresponding to the base stations,
† Vch ¼ {ch11 ; ch12 ; …; chCN N } is the set of vertices where chjk corresponds to channel1 j being supported under base station Bk ; † Vm ¼ {m1 ; m2 ; …} is the set of vertices corresponding to active mobiles in the system, † E1 ¼ {ðs; mi Þlmi [ Vm }; E2 ¼ {ðmi ; chjk Þ} such that mobile mi can potentially use channel chjk ; E3 ¼ {ðchjk ; Bk Þlchjk [ Vch ; Bk [ Vb }; E4 ¼ {ðBk ; tÞlBk [ Vb } Let there be K classes of multimedia services supported by the network where a call of class k ð1 # k # KÞ initiated by mobile mi ; requires minimum of lki and a maximum of uki channels. We construct the flow network, GF ¼ ðV; EÞ; for DMCA, such that V ¼ {Vm < Vb < Vch < {s; t}} and E ¼ {E1 < E2 < E3 < E4 }: The terms ‘mobile’, ‘base station’ and ‘channel’ will be used to also refer to the corresponding vertices in the flow network. Given the set of edges and vertices as above, assignment of lower, upper capacity and cost values to edges is done as follows. Cost(c): For edges from the source ðsÞ to mobiles and base stations to the sink ðtÞ; the cost is set to zero. For edges from the mobiles to channels, the cost is set to the inverse of the carrier to interference ratio (CIR), that the mobile will experience when using the corresponding channel (denoted by Rmi ðv; wÞ). This interference is caused by down-link transmissions of other base stations that use the same channel while the carrier strength is the received signal strength from the candidate base station, (see Appendix for signal propagation and interference calculations). For edges from the channels to base stations, the cost is set to the interference level that the base station will experience when using the corresponding channel (denoted by RBk ðv; wÞ). This interference is caused by up-link transmissions of other mobile users that use the same channel. Upper Capacity(u): For edges from the base stations to the sink, the upper capacity is set to the respective number of channels supported under each base station. For edges from mobiles to channels and from channels to base stations, it is set to 1. For edges from the source to mobiles, the upper capacity is set to the maximum number of channels required by the respective mobile for its service class. Lower Capacity(l): For edges from base stations to the sink, from mobiles to channels and from channels to base stations, the lower capacity is set to zero. For edges from the source to mobiles, it is set to the minimum number of channels required by the respective mobile for its service class. Example 1. Fig. 1 illustrates a flow network corresponding to base stations (B1 and B2 ), each supporting three channels. We assume that there are active mobiles under 1 A channel in our framework consists of an up-link and a down-link portion which are predetermined pairs.
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
419
Fig. 1. Flow network example.
neighboring base stations but there is currently one mobile user which just became active under base station B1 and there is no active mobile under base station B2 : The corresponding flow network also implies that the mobile m1 can potentially use channel ch11, ch21 or ch31. The triplet of values associated with each edge of this network corresponds to the l; u; and c values of that edge. In this flow network, one unit of flow pushed from the source to the sink corresponds to an assignment of a particular mobile to a channel under a base station. In other words, at any instance of time, a maximum possible flow from s to t (max-flow) induces a set of assignments where each element of this assignment is a triplet of (mobile, channel, base station). Given an instance of GF ; we can employ a max-flow algorithm to find the assignment set whose cardinality is maximum.
the mobile will communicate with; the set of channels, Vch ; that can potentially be used by the mobile and their corresponding interference levels, Rmi : Next the flow network is expanded by adding edges from the mobile node mi to the nodes corresponding to the candidate channels in Vch : While doing so, no edge is added to the channels for which the interference level is above a threshold value. For each edge added to the flow network, its cost is assigned as the corresponding interference level in Rmi : Then we attempt to find as many minimum-cost augmenting paths from the source to the sink as the minimum number of channels, lki ; required by the mobile such that the augmenting paths include the new mobile. This requires finding lki many shortest paths from s to t that goes through mi : If we can not find lki many paths, the new call is blocked since the base station can not provide enough channels for the mobile to start its communication. Fig. 2 illustrates the flow chart for the algorithm. In call admission
3. Dynamic multi-channel assignment algorithm (DMCA) In this section, we explain our system model and how to utilize flow networks for DMCA. We describe in details the two-stage algorithm for DMCA. Each base station controller (BSC) in the system constructs a flow network GF ¼ ðV; EÞ as explained in Section 2. The channel assignment algorithm then proceeds with different trigger events being handled differently. 3.1. DMCA-first stage When a new call arrives, it has to be admitted by incurring as little cost as possible. In our case, the cost is the experienced interference by the communicating parties. The algorithm starts with expanding the flow network GF such that a new vertex is created for the new mobile. Let mi be the new mobile that requests service from the system. At the time of a call arrival, the BSC knows which base station, Bk ;
Fig. 2. Flowchart for DMCA-first stage.
420
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
Fig. 3. Actual flow after DMCA-first stage.
attempt, the algorithm does not perform a global computation on the flow network that would slow down the response time dramatically. Instead, it performs a local augmentation of the flow to find a channel that can be assigned to the new mobile. Furthermore, an upper threshold ðLÞ on the path length can be set to prevent the shortest path algorithm considering long paths that would cause reassignment of several other mobiles to other channels or base stations. Fig. 3 illustrates the actual flow from the source to the sink after the execution of the first stage of the algorithm on the flow network of Example 1 (since base station B2 is not involved in our running example it is not shown in the rest of the figures). This flow structure corresponds to the assignment of the channels ch11 and ch31 to the mobile m1 under base station B1 : Fig. 4 illustrates the structure of the corresponding residual network. In this residual network, the backward edges (dark-colored edges) appear which are not a part of the original flow network. These edges represent the potential for pushing back (canceling) the existing flow in the network. Costs of such edges are negative since canceling an existing flow would also eliminate the associated cost. As will be explained later, canceling one unit of flow would correspond to a reassignment of a channel, since the cancelled flow would be re-routed to another channel and/or a base station. Based on the assignment outcome for our example, mobile m1 is assigned to the maximum number of channels that it requested (m1 has requested a minimum of one and a maximum of two channels). This implies that the system should be able to reassign one of m1 ’s channels if and when it is required by other mobiles under heavy traffic load. In other words, the channel assignment algorithm should be capable of degrading m1 ’s service for the sake of admitting
other mobiles to the system. This is addressed by the second stage of the algorithm. 3.2. DMCA-second stage Once the incoming call is accepted, we perform the second stage of the DMCA algorithm. The purpose of this stage is to modify the structure of the residual network to enable the degradation or improvement of the assignment for the newly accepted mobile mi and to modify the cost structure to include the reassignment penalties. To enable the degradation of the assignment of mobile mi ; we create a (redundant) vertex di associated with mi and add the following edges to the residual network. An edge ðmi ; di Þ with a lower capacity of l ¼ 0; an upper capacity of u ¼ f ðs; mi Þ 2 lik and a cost c ¼ cmax þ 1 where cmax is the maximum possible edge cost in the graph. We also add an edge ðdi ; tÞ with l ¼ u ¼ c ¼ 0: In order to incorporate the cost of reassignments, we add the value of ak to the cost of the backward edges ðchjk ; mi Þ in the residual network (that have non-zero flow in the flow network). The intuition behind this is that, in order to reassign a channel chjk from mobile mi to another mobile ml ; the new mobile ml has to have at least ak units less than the interference level of mi : This is the penalty that has to be paid for a reassignment. Fig. 5 illustrates the residual network for Example 1 after the above transformation with ak ¼ 3: Intuitively, f ðs; mi Þ represents the number of channels currently assigned to a mobile mi and ðf ðs; mi Þ 2 lik Þ is the number of channels that mi may be forced to sacrifice by the BSC to accommodate other users. However, due to the way the upper capacity bound is assigned, the mobile can not be forced to give up channels so that it occupies less than its minimum bandwidth requirements. The cost assignment of c ¼ cmax þ 1 to
Fig. 4. Residual network after DMCA-first stage.
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
421
Fig. 5. Residual network after DMCA second stage.
the edge di prevents unnecessary degradation of mi ’s assignment while there are other channels available.
and the flow values are updated as follows: † Delete edges ðs; mi Þ and ðmi ; chjk Þ:
Example 2. In Fig. 6 another mobile m2 just became active and requests channels from the system. Also m2 requires exactly two channels for its service class (for clarity only edge costs and relevant channels are shown in the figure). The first stage of the DMCA algorithm will find the first path P1 as ks; m2 ; ch11 ; B1 ; tl with a total cost of 30, and the second path P2 as ks; m2 ; ch11 ; m1 ; d1 ; tl with a total cost of ð37 2 12 þ cmax þ 1 ¼ cmax þ 26Þ: The other candidate path ks; m2 ; ch31 ; m1 ; d1 ; tl has a cost of ð27 2 1 þ cmax þ 1 ¼ cmax þ 27Þ which eliminates it from being the second shortest path. Pushing one unit of flow through P2 will reassign ch11 from mobile m1 to mobile m2 : While satisfying the minimum channel demand of m2 ; this reassignment downgrades the assignment of m1 by one channel. This reassignment is reflected in the residual network of Fig. 7.
3.3. Call termination On termination of mobile mi ’s call, the corresponding vertex and adjacent edges for that mobile are deleted
† Decrement flow value of all edges (chlk ; Bk ) where chlk is the channel mi was using. For each such channel, decrement the flow value of the edge (Bk ; t:) 3.4. Reassignment (handoff) Whenever a mobile mi ; who is using channel chjk ; begins to experience an intolerable interference, it notifies the BSC and the system has to reassign mi to another channel (possibly under another base station). At this point, the BSC updates the network by deleting the edge ðmi ; chjk Þ and then executing a shortest path algorithm to find another augmenting path. If such a path exists, the mobile is reassigned to the corresponding channel on the path. Otherwise, if loosing chjk decrements the number of channels to below lik ; the ongoing call is dropped. This first type of reassignment is mobile-assisted and triggered by the fact that the mobile is experiencing high interference. When a mobile notifies a BSC of high interference, it also provides a list of channels that it can potentially use and a base station id which it receives the strongest signal from.
Fig. 6. Residual network after mobile m2 arrived.
422
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
Fig. 7. Residual network after mobile m2 is accepted.
The second type of reassignments is initiated by the base station based on the interference experienced on the uplink channel. When the ratio RB of received interference to carrier strength is above a threshold over a particular channel, it triggers a reassignment in which case the BSC removes the edge from the channel to the requesting base station and runs a shortest path algorithm on the residual network from the mobile which was using the channel. If it finds a path that goes through the initiating base station, it augments the flow accordingly in which case the uplink channel is handed off gracefully. Otherwise, loosing the uplink channel may degrade the bandwidth or cause a call drop. Reassignments that are initiated by the mobiles or the base stations can be either within the same cell (intra-cell reassignment) or between two neighboring cells (inter-cell reassignments). Intra-cell reassignments incur a penalty of a into the overall cost and this penalty can be used to control the reassignments in the system. Similarly, inter-cell reassignments incur a penalty of b: These parameters are system-wide and facilitate the fine tuning of the reassignment rates.
corresponding base station and when borrowing occurs the BSC removes the incoming edge to the donor base station (and all other cells that needs to be prohibited), re-creates it for the borrowing base station. This mechanism explicitly locks the borrowed channel. 4.2. Distributed channel assignment schemes ([5,12,13]) When the flow network is constructed per base station, the distributed algorithms are easily modeled. Each base station constructs flow network for its supported channels. Since the cost function is based on the Rm and RB values and interference measurements are done independently by each base station and mobile, the cost assignments are as explained before. The inter-cell handoffs are handled by the BSC. 4.3. DCA schemes ([5,7,10,11]) The main idea of all DCA schemes is to evaluate the cost of using each candidate channel, and select the one with the minimum cost provided that certain interference constraints are satisfied. The selection of the cost function is what
4. Network flow framework and existing algorithms One attractive feature of the proposed network flow framework is that it is able to model several different variants of the channel assignment algorithms reported in the literature. In this section we will present some examples of how this model captures several properties of other algorithms. 4.1. Channel borrowing schemes for FCA ([2,14,15]) In a channel borrowing scheme, a base station that has used all its assigned channels can borrow free channels from its neighboring cells. Several other cells are prohibited from using the borrowed channel by locking the channel in those cells. This is to ensure avoidance of channel interference. Creating the flow network for FCA with channel borrowing requires that each channel has an edge to its
Fig. 8. Base station layout.
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426 Table 1 Network services used in simulations Traffic class
Channels required
Calls (%)
Average connection time
Example
1 2 3 4 5
1 5–10 1–10 8–25 5–15
75 5 10 3 5
1.5 min 5 min 30 s 10 min 3 min
Voice services Video phone/conferencing E-mail, paging, fax Interactive multimedia File transfer, remote login
differentiates DCA schemes from each other. Our proposed algorithm is based on the interference measurement. However, the network flow model handles the call arrivals and handovers gracefully independent of what the cost function is. One example of such cost functions is the future blocking probability in the vicinity of the cell in which the call is initiated [10,11]. In our framework, based on the history of the system, the BSC can assign more cost to the edges to/ from nodes corresponding to such channels that caused high call blocking in the vicinity. 4.4. Deadlock and instability prevention Existing algorithms (so is the one presented in this paper) that employ the interference measurement and adaptation schemes may suffer from instability in which an assignment decision made locally can have ripple affect by increasing the interference experienced by several ongoing calls in the neighboring cells. An accepted call in one cell may trigger reassignments in several other cells and the overall system may never converge to a stable state. Although the algorithm presented in this paper guarantees that a newly accepted call would not reduce the number of channels that are already acquired by other mobiles below their lower bound, it does not predict the system-wide effect and does not predict the interference effect on the acquired channel in the neighboring cells.
423
However, as stated earlier, in our network flow model, assignment or reassignment of certain channels can be discouraged by selectively assigning higher costs to edges incident to those channels. The trade-off between avoiding call blocking and avoiding service interruptions (call drops) can be fine tuned and reflected in the model. One such algorithm is to limit the number of reassignments that would be incurred when trying to accept a new mobile into the network. By varying the number of acceptable reassignments (this can be achieved by limiting the number of mobile nodes visited in the shortest augmenting path algorithm), the system performance can be fine-tuned.
5. Simulation results We have simulated our DMCA algorithm over a real cellular network with coverage area of 54 base stations that represents an actual metropolitan area (Fig. 8). Traffic data is based on collected busy-hour call attempts in the coverage area. The following parameters are used in the simulation: † † † † † †
Call arrival rate Call holding time Minimum acceptable C/I ratio Intra-cell reassignment penalty ðaÞ; Inter-cell reassignment penalty ðbÞ; Number of channels supported in each base station.
In order to represent different multimedia applications, five different traffic classes are assumed based on the connection duration and bandwidth requirement (Table 1). These are typical applications seen on existing networks. Call arrival and handoff rates are driven from the collected traffic data which represented 52,000 calls/h. Figs. 9 and 10 illustrate the blocking/dropping probabilities for each traffic class under non-uniform traffic patterns for limited and unlimited number of reassignment thresholds, respectively. As explained before, setting
Fig. 9. Number of handoffs limited to 3.
424
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
Fig. 10. Unlimited number of handoffs.
a limit on the number of inter/intra-cell reassignments prevents a system-wide instability but also as seen in the charts, compromises the blocking probability. As expected, this reassignment limit does not have as much impact on the call drop rate as the blocking rate. Lower bandwidth service classes, however, are impacted by the limit more than the higher bandwidth service classes. This same effect is not observed when we set no limit on the reassignments but assign higher reassignment penalties. In the latter case, when an augmenting shortest path is to be found, the algorithm performs the reassignment even though the total cost of the path is higher (since it is still a path from the source to the sink no matter how costly it is). We have also experimented on limiting the number of channels that a higher bandwidth class mobile can acquire (between its min and max range) when it is first accepted into the network. This did not have noticeable performance impact on the system other than a negligible improvement on the drop rate. Another observation is that, services that require higher bandwidth have higher blocking probability but once they are admitted into the system, the algorithm attempts to keep the assigned channels (potentially blocking other calls); that is why these traffic classes have less dropping probability compared to their blocking probability. Figs. 11 and 12 illustrate the performance of the algorithm in comparison with FCA under non-uniform
and uniform traffic patterns. For non-uniform traffic pattern, the traffic intensity over each cell is determined randomly. For FCA algorithm, the frequency reuse pattern that determines the cluster of cells that a channel can not be reused (see Ref. [3] for details). Another set of experiments is done on the call setup time performance of the DMCA. Call setup time is the time it takes for the system to establish the connection for the call (in our case assign required number of channels) from the time the call has arrived. The comparison to the call setup time of FCA with a reuse factor of 7 (denoted by GFCA ) is illustrated in Fig. 13. As expected, the DMCA takes longer to establish the call as compared to the FCA, since the decision in FCA is straightforward. Also if the number of reassignments are not limited, as the load is increased, the DMCA call setup performance degrades whereas when the reassignments are limited, the call setup time stabilizes. Call setup time performance of the DMCA is a tradeoff between increased capacity versus the response time.
Fig. 11. Performance under non-uniform load.
Fig. 12. Performance under uniform load.
6. Conclusion In this paper, we presented a network flow based framework and an algorithm for DMCA which uniformly handles different types of traffic classes requiring different number of channels. In particular, upper and lower capacity
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
425
loss for received power and interference calculations. The CIR for a mobile, mi ; is defined as
C ðB Þ Rm i ¼ X r C Cr ðBt Þ t[IB
where, Cr ðBÞ is the received signal power (dBm) from base station B as measured by the mobile mi ; BC is the candidate base station, and IB is the set of interfering base stations. For the candidate base station:
Fig. 13. FCA-to-DMCA call setup time ratio ðGFCA =GDMCA Þ:
limits in the flow network captures the minimum and maximum number of channels required by different types of traffic classes. This framework not only captures several fundamental aspects of wireless mobile networks and handles the channel assignment related events in the system gracefully but also uses a realistic cost model. It also has several parameters that can be fine-tuned to improve different performance objectives. The algorithm presented, makes the assignment decision through local computations on the flow graph rather than global reorganization of the existing assignment. Instead of running a min-cost max-flow algorithm from scratch, the algorithm runs a shortest path algorithm from source node to the sink whose locality can be fine tuned by limiting the number of reassignments. The number of intra- and inter-cell reassignments can easily be limited to a desired threshold (due to the layered structure of the flow network) to prevent reassignments leading to instability in the network. Our model supports multiple traffic classes and suitable for multi-service networks. The degradation and upgrade of an existing calls for active mobiles within their respective traffic class limits are handled seamlessly and can be easily adapted to distributed systems.
Appendix A Computation of signal propagation parameters is an important part of the simulation since our channel assignment algorithm uses the CIR ratios experienced by the candidate mobile and the candidate base station in determining the edge costs in the flow network. For this purpose, it is necessary to calculate predicted values of received power (signal strength) at a particular distance. The candidate mobile will experience interference due to the co-channel base stations of its own candidate base station. Similarly, the candidate base station will experience interference from the mobiles in the neighboring base stations that use the same frequency as the candidate mobile. In our model we assumed a dense urban area path
C ðm Þ RB C ¼ X r i Cr ðmj Þ j[Im
where, Cr ðmÞ is the received signal power (dBm) from mobile m as measured by the base station Bc ; mi is the candidate mobile and Im is the set of interfering mobiles. We have used an 8 dB log-normal standard deviation over the mean power values [3]. In our simulations, we have used ETSI Cost-231 Walfish-Ikegami model for small cells in the range of 200 m to 3 km and COST-231 Hata model in ranges over 3 km [6]. When using these models, we have fixed several parameters for simplicity such as antenna heights, building height assumptions, etc. Although we do not explicitly use terrain data in our simulations, COST-231 models have effects of building heights, width and direction of the roads, multi screen diffraction and scatter loss inherent in them. We only considered the omni-directional base station sites, therefore we do not take advantage of directional antenna interference reduction properties. We assume all the mobiles are of the same power class with the assumed maximum power of 2 W (33 dBm) and all the base stations have maximum power of 20 W (43 dBm).
References [1] L.R. Ford Jr., D.R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, 1962. [2] S.K. Das, S.K. Sen, R. Jayaram, A novel load balancing scheme for the tele-traffic hot spot problem in cellular networks, Wireless Networks (WINET) 4 (4) (1998) 325– 340. [3] W.C.Y. Lee, Mobile Cellular Telecommunications: Analog and Digital Systems, McGraw-Hill, New York, 1995. [4] T.S. Rappaport, Wireless Communications Systems, IEEE Press, New York, 1996. [5] A. Lozano, D.C. Cox, Distributed dynamic channel assignment in TDMA mobile communication systems, IEEE Transactions on Vehicular Technology 51 (6) (2002) 1397– 1406. [6] ETSI Technical report ETR 364, Digital Cellular Communications System: Radio network planning aspects, November 1996. [7] J.C. Chuang, Performance issues and algorithms for dynamic channel assignment, IEEE Journal on Selected Areas in Communication 11 (6) (1993). [8] O. Koyuncu, S.K. Das, H. Ernam, Dynamic resource assignment using network flows in wireless data networks, 49th IEEE Vehicular Technology Conference, vol. 1, 1999, pp. 1–5. [9] O. Koyuncu, S.K. Das, H. Ernam, Design and implementation of a dynamic channel assignment algorithm using network flows, Proceed-
426
S.K. Das, O. Koyuncu / Microprocessors and Microsystems 28 (2004) 417–426
ings of Second International Workshop on Discrete Algorithms and Methods for Mobility, Dallas, Texas, October 1998. [10] M. Zhang, T.-S. Yum, The non-uniform compact pattern allocation algorithm for cellular mobile systems, IEEE Transactions on Vehicular Techology VT-40 (1991) 387–391. [11] M. Zhang, Comparisons of channel assignment strategies in cellular mobile telephone systems, IEEE Transactions on Vehicular Techology VT-38 (1989) 211 –215. [12] M. Frodigh, Reuse partitioning with traffic adaptive channel assignmentfor highway microcellular radio systems, Proceedings of GLOBECOM (1992) 1414–1418.
[13] C.W. Sung, K.W. Shum, Assignment and layer selection in hierarchical cellular system with fuzzy control, IEEE Transactions on Vehicular Technology 50 (3) (2001) 657–663. [14] V.T. Vakili, A. Aziminejad, A new channel borrowing assignment scheme: teletraffic performance evaluation through discrete event modeling in a mobile cellular environment, Proceedings of the 7th International Conference on Telecommunications, vol. 1, 2003, pp. 279–286. [15] S. Mitra, S. DasBit, A load balancing strategy using dynamic channel assignment and channel borrowing in cellular mobile environment, IEEE International Conference on Personal Wireless Communications, December 2000, pp. 278 –282.