Modeling and Analysis of a Shared Channel Architecture for Performance Improvement in Optical Burst Switched Networks

Transcription

1 Modeling and of a Shared Channel Architecture for Performance Improvement in Optical Burst Switched Networks Wyatt Chaffee, Bin Wang, Haining Wang Department of Computer Science and Engineering Wright State University Dayton, Ohio Department of Computer Science The College of William and Mary Williamsburg, Virginia 2387 Abstract Existing optical burst switching (OBS) architecture has assumed the separated transfer of burst header packets and data bursts. To deal with burst contention and blocking, various approaches have been proposed such as using deflection routing, fiber delay line buffering, wavelength conversion, and burst segmentation. In this paper, we investigate a shared channel architecture that allows the transfer of both burst header packets and data bursts on the same wavelength channel with some modifications on the current OBS architecture. The new shared channel based OBS architecture is expected to have better flexibility in resource utilization and improved burst blocking performance. Based on the reduced load fixed point approximation, we provide an analytic model for burst blocking probability analysis under the proposed architecture which employs the just-enough-time signaling and fixed routing. The accuracy of the analytic model is validated via extensive simulation. Overall, our analysis and simulation show that the proposed architecture achieves a significantly lower burst blocking probability than the conventional architecture. Introduction Optical burst switching (OBS) [, 2, 4, 20, 2] has been proposed as an optical switching paradigm to combine the best of optical circuit and packet switching while avoiding their shortcomings. OBS employs statistical multiplexing of bursts, thereby improving bandwidth efficiency and core scalability over wavelength routing. Under OBS, client traffic is encapsulated into data bursts (DBs) at the ingress OBS nodes and decapsulated at the egress OBS nodes. The control information describing where and how the DB should be forwarded and when it will arrive is contained in a separate control packet (a.k.a. burst header packet (BHP)). Usually, a BHP is sent on a control wavelength with an offset time (i.e., a lead time) before the transmission of the corresponding data burst, in order to allow the BHP to be processed at each intermediate node to reserve resources and configure the switches along the route for the data bursts before their arrivals. Fiber delay line (FDL) requirements can therefore be eliminated. Various OBS signaling protocols have been developed over the years, including just-in-time (JIT) [8], just-enough-time (JET) [2], JumpStart [9], and so on. Multiple channels are multiplexed on an optical fiber using the technique of wavelength division multiplexing (WDM). Existing optical burst switching (OBS) architecture (termed as the conventional OBS architecture hereafter) [2,, 2, 4, 9, 20] has assumed that data and control signals are transmitted separately on different channels or wavelengths, where a group of wavelengths usually called the data channel group (DCG) is established for the transfer of DBs and another group called the control channel group (CCG) is established for the transfer of BHPs. In such an architecture, costly O/E/O conversions are only required on a few control channels instead of a large number of data channels. However, burst contention and blocking are key issues that have attracted much recent research. A burst contention occurs at a switch whenever two or more bursts are trying to leave the switch from the same output port on the same wavelength. In electrical packet switched

2 networks, contentions are usually resolved with the storeand-forward technique, which requires the packets in contention be stored in a memory bank and sent out at a later time when the desired output port is free. This has not been possible in all optical networks because of the unavailability of optical RAM. Many contention resolution schemes for OBS networks have been proposed. These schemes make use of deflection routing [4, 6], fiber delay line buffering [5, 0], wavelength conversion [6, 22], and burst segmentation [5, 6]. To deal with burst contention and blocking as well as to achieve greater resource utilization, in this paper, we investigate a shared channel architecture that allows the transfer of both burst header packets and data bursts on the same wavelength channel with some modifications on the conventional OBS architecture. The proposed OBS architecture is expected to provide better flexibility in resource use and improved burst blocking performance. Based on the reduced load fixed point approximation, we provide an analytic model for burst blocking probability analysis under the proposed architecture that employs the just-enough-time signaling and fixed routing. The accuracy of the analytic model is validated via extensive simulation. Our analysis and simulation show that the proposed architecture achieves a significantly lower burst blocking probability compared with the conventional architecture. We also showed that the best configuration of the conventional architecture depends on the load, average data burst size, and total number of channels. Therefore, the proposed OBS architecture is easier to configure and achieves better overall performance. The rest of this paper is organized as follows. Section 2 describes our proposed shared channel OBS architecture. In Section 3, we present our analytic model based on the reduced load fixed point approximation. The analysis is then validated via extensive simulation in Section 4. In Section 5, we discuss our results of performance study. Section 6 contains our concluding remarks. 2 Shared Channel Architecture Achieving the best resource utilization and burst blocking performance in an OBS network can be seen as a multivariate optimization problem. Among the variables are the numbers of wavelength channels assigned for the purpose of BHP transmission and DB transmission, respectively. Usually the best solution to an optimization problem is not an integral one. In other words, the best solution for OBS networks may feature a non-integer number of control and data channels. This motivates us to look at alternative OBS architectures. We propose a shared channel OBS architecture. In this architecture, BHPs and DBs are permitted to travel on any available wavelength in the network. Thus DBs may use channels normally assigned to BHPs in the conventional OBS architecture and vice versa. The only restriction is that two transmissions do not occur at the same time on the same output channel. It would also be possible to offer only a portion of the total number of channels as shared while reserving the remaining channels for a specific transmission type (i.e., DB or BHP). We leave this possibility for future investigation. The implementation of our shared channel architecture (Fig. ) requires some modifications on the conventional OBS architecture (e.g., the OBS architecture of [9]) to reduce the costly O/E/O conversion required on a large number of data channels. We assume there exists a device called optical header differentiator (OHD) that can optically detect and distinguish whether the incoming signal is a BHP or a DB on a wavelength channel. Note that only optical header detection and differentiation capability, not complete optical header processing capability, is assumed. A switching mechanism is employed on each incoming wavelength in combination with the optical header differentiator to form a dynamic channel mapping unit. If the optical header differentiator on a wavelength determines that the incoming signal is a BHP, the switching mechanism forwards the incoming signal to the Switch Control Unit (SCU) for O/E/O conversion and processing. Otherwise, the incoming optical signal is delivered to the optical switching matrix for optical switching in much the same way an optical signal is forwarded to FDLs for buffering in the conventional OBS architecture. Once a BHP has been processed by the SCU, receiving the corresponding DB should not be a problem. Armed with the arrival time and the channel information of the incoming DB, the dynamic channel mapping unit will adjust such that the DB is forwarded into the optical switching matrix appropriately. Both the SCU and the optical switching matrix operate in much the same way the SCU and optical switching matrix operate in the conventional OBS architecture. The cost of our proposed system mainly depends on the amount of O/E/O conversion employed. In the worst case, each channel needs O/E/O conversion which is not desirable. The cost may be reduced by enabling wavelength channels to share O/E/O conversion which may lead to BHP loss due to contention. FDLs can then be employed to buffer BHPs effectively since the size of BHPs is small, resulting in no or very low BHP loss with properly dimensioned FDL buffers. The O/E/O conversion may also be tunable. This work, however, performs initial simulation studies assuming no BHP loss due to O/E/O contention. In addition, we also assume a pure loss model for the switching of the BHPs in the analytic model without considering the potential buffering of BHPs. Allowing a short queue of the BHPs can reduce the BHP loss significantly in the analysis. The tradeoffs between the O/E/O cost and system performance

3 Fiber N Channel FDL buffer. DCG. CCG Dynamic Channel Mapping Unit Optical Switching Matrix Switch Control Unit Routing & signaling processors. DCG. CCG Figure. The proposed shared channel OBS architecture with the dynamic channel mapping unit. Note that DCG and CCG are dynamically determined by the channel mapping unit. will be further studied in the future work. The complexity of our proposed system should not be significantly more than the conventional OBS architectures which employ fiber delay lines, as a similar switching device is necessary to forward a transmission to the correct FDL; and O/E/O conversion is only conducted for BHPs in the shared channel OBS architecture. The only additional capability required in the proposed OBS architecture is the optical header differentiators. Optical header recognition and processing is one key function that enables ultrafast optical routing in photonic packet-switched networks. Many researchers have already proposed and/or demonstrated novel cost effective approaches to optical packet header recognition and processing [, 3, 7, 8, 7]. The dynamic channel mapping unit in our proposed architecture does not require full-fledged optical header processing; therefore incurs lower cost. To illustrate our proposed architecture, we modify the presentation of OBS control architecture presented in [9] to reflect these changes in Fig.. Note that DCG and CCG are dynamically determined by the channel mapping unit. 3 Analytic Performance Modeling In this section, we provide an analytic model for studying the burst blocking probability of the proposed shared channel OBS architecture as well as the conventional OBS architecture. The analysis utilizes a technique based on the reduced fixed point approximation [3] to calculate the multihop blocking probability. We consider a network with J directional links, labeled from to J. Link j has F j optical fibers. Each fiber can M carry traffic on W wavelengths simultaneously. Thus the total number of wavelength channels for link j is N j = W F j. In this work, we assume that fixed routing is used to simplify the analysis. Specifically, let R be a set of all possible routes in the network. A route r is an ordered set of links connecting a source node and a destination node. The offered bursts to route r arrive following a Poisson process with a rate of λ r. Traffic is delivered from a source node towards a destination node along route r. A burst offered to route r uses a single-wavelength channel from each link along the route until it is blocked and dropped or until it exits the network. We assume that burst transmission times are independent and exponentially distributed. We also allow for varying bandwidth capacities on each link. Let µ j be the transmission rate of link j measured in bursts per unit time. Our goal is to evaluate the stationary blocking probability of a burst offered to route r and of an arbitrary burst. We make the standard assumption that each blocking event occurs independently from link to link along any route. We use B = (B, B 2,..., B J ) to denote the vector of stationary link burst blocking probabilities. Define an indicator function I(i, j, r) that returns one if links i, j are on route r (i.e., i, j r) and link i precedes (not necessarily immediately) link j on route r; otherwise I(i, j, r) returns zero. Based on these assumptions, it follows that the offered load to link j, ρ j, is given by, ρ j = µ j r R:j r λ r J i= ( I(i, j, r) B i ). () Based on the independence assumption, we may assume that the offered load to link j is a Poisson arrival process with rate ρ j. Therefore, the burst blocking probability is given by the Erlang formula, B j = E(ρ j, N j ) = ρn j j /N j! Nj (2) k=0 ρk j /k!. Plug in Eqn. () to Eqn. (2), we have the following fixed point equations satisfied by the approximate link burst blocking probabilities, B j = E(µ j r R:j r λ r J i= ( I(i, j, r) B i ), N j ). (3) Assuming that the link burst blocking probability vector B is solved from Eqn. (3), we can use the following equation to compute the burst blocking probability along route r due to link independence, B(r) = i r( B i ).

4 The overall burst blocking probability can then be computed as B = λ r B(r), Λ r R where Λ = r R λ r. To solve these fixed point equations for the stationary link burst blocking probabilities, an iterative substitution process is used. For any given vector of blocking probabilities B, define the transformation vector T(B) = (T (B), T 2 (B),..., T J (B)) where T j (B) = E(µ j r R:j r λ r J i= ( I(i, j, r) B i ), N j ). After having set an initial link blocking probability vector B 0 = B 0, the transformation T(B) is applied repeatedly. That is, we can perform B n = T(B n ) where n =, 2,... and B 0 = B 0 until B n is sufficiently close to B n. Thus far, the analysis has been used to approximately compute the blocking probability of a single type of traffic in the network, i.e., the blocking probability of DBs assuming that there is no blocking of BHPs. Determining the blocking probability of both DBs and BHPs in the conventional OBS architecture (with separate DCG and CCG) as well as in the proposed shared channel OBS architecture will require some additional steps. Although arrivals are assumed to be independent, we may assume that a BHP and a DB arrive in a pair. If either the BHP or the DB is blocked, we consider the transmission as a whole unsuccessful. Let D j be the number of data channels on link j in the conventional OBS architecture, N j D j the total number of control channels on link j, and /E(DB j ) service rate of DBs at link j where E(DB j ) is the average DB size (in seconds) on link j. We assume the average BHP size is E(BHP j ) (in seconds). Let the departure rate of link j to be the departure rate of DBs at link j. Since the departure rates of DBs and BHPs are not the same, we will see shortly how this affects our analysis. Let the arrival rate of traffic to route r, λ r be the arrival of paired BHP and DB transmissions to route r. The arrival of BHPs will occur at the same rate λ r since it will always be considered by the switch immediately upon arrival. Therefore λ BHP r = λ r. Although DBs arrive along with BHPs in pairs, we cannot say that the actual DB arrival rate to a link is the same as BHP because the DB will only be considered when the switch has been configured by a successfully processed BHP. Using Eqn. (), we can calculate the BHP traffic intensity ρ j. Recall that ρ j will contain the DB departure rate instead of the BHP departure rate in the denominator. We can make the analysis accurate by dividing ρ j with the ratio of the DB size to BHP size. Specifically, using Eqn. (2) with ρ j /(E(DB j )/E(BHP j )) and with N j D j channels, we can determine the blocking probability of BHPs as: B BHP j = E(ρ j /(E(DB j )/E(BHP j )), N j D j ). (4) Since a DB can only be processed if its corresponding BHP has been successfully processed, the rate of incoming DBs is determined by the number of BHPs that can be processed and placed onto outgoing channels. Thus, we must consider the BHP blocking rate when determining the incoming DB rate. The Poisson arrival rate that should be used when calculating the DB blocking probabilities is simply the rate of incoming transmissions minus the rate of incoming transmissions multiplied by the BHP blocking probability, or ρ j ρ j Bj BHP, which indicates the fact that there is a Bj BHP probability that an arriving transmission will not make it past the BHP processing. We can then obtain the blocking probability of DBs on link j from Eqn. (2) using ρ j ρ j Bj BHP as the Poisson arrival rate with D j channels: B DB j = E(ρ j ρ j B BHP j, D j ). (5) We may now utilize Bj BHP and Bj DB to determine the total blocking probability of a transmission. Let the probability that a transmission on link j is successful be represented by P j. Let Pj BHP and Pj DB represent the probability that a BHP and a DB on link j is successfully transmitted, respectively, we have: P BHP j = Bj BHP, Pj DB = Bj DB, P j = P BHP j P DB j. It is then easy to obtain the blocking probability of a transmission using Eqn. (6): B j = ( Bj BHP ) ( Bj DB ). (6) In the conventional OBS architecture, the number of DBs processed by the OBS switch is determined by the number of BHPs that can be processed without contention. This is true in the proposed shared channel OBS architecture. What is different about the proposed OBS architecture is that the number of BHPs blocked is also affected by the number of DB arrivals on the same wavelength channel due to channel sharing, a property which can make analysis difficult. To simplify the analysis, we first assume that the number of DBs arriving for processing is equal to the number of BHP arrivals to the node. This should provide an upper limit for the blocking probability at that switch. The offered load to the node will be the sum of the load of BHPs and the load of DBs. The load of BHPs is then adjusted by a ratio of average DB size to average BHP size to account for the fact that the departure rate of BHPs is not equal to the

5 departure rate of DBs. The resulting departure rate will be the new arrival rate for transmissions at the next node on the route. Since all the channels are available to the shared channel OBS architecture, we use N j in the Erlang B formula and the adjusted combined load of BHPs and DBs, ρ j + ρ j /(E(DB j )/E(BHP j )). The blocking probability for the shared channel OBS architecture can be then calculated as: 2 4 R = , R3 = , R5 = , R7 = , R9 = , R = , R2 = R4 = R6 = R8 = R0 = R2 = B j = E(ρ j + ρ j /(E(DB j )/E(BHP j )), N j ). (7) Since a BHP and a DB are combined in a pair, the blocking probability given by our analysis is the probability that either one of these is blocked. Our analysis does not consider the amount of processing time incurred by the dynamic channel mapping unit. We believe that this time would be small; and therefore exclude this from our calculations in an attempt to keep the analysis as simple as possible. 4 Model Validation In this section, we validate our analytic model via extensive simulation. Our simulation and analysis utilize the 3-node NSFNET topology [3] and feature traffic traveling along the routes shown in Fig. 2. In the simulation, DBs are sent a sufficient period of time after BHPs to allow enough time for processing at each hop. We simulate an OBS network using the just-enough-time signaling and the latest available unused channel with void filling (LAUC- VF) scheduling algorithm [9]. The size of BHPs is assumed to be 52 bits. The transmission rate of each channel is,000,000 bits per second. Arrival times of DBs and BHPs are assumed to be independent in the analysis. In the simulation, the arrival times of corresponding DBs and BHPs are dependent. The arrival time of a DB depends on the arrival time of the corresponding BHP since the DB arrives an offset time after the BHP. Switching time is not considered by our scheduler. All simulations were run to 95% confidence. Error bars are not shown in the figures for clarity of presentation. 4. Effect of Number of Channels Table shows the results of simulation and analysis using an arrival rate of 30 burst transmissions per second and a total eight channels per uni-directional link. The average size of the DBs is 40,000 bits. Each channel can process 25 DBs per second. This corresponds to approximately a load of 5% of the total network capacity. That is, the load is calculated as the fraction obtained by dividing the arrival rate by total link processing capacity which is given by multiplying the departure rate of each channel with the 3 5 Figure 2. NSFNET topology and routes. Table. Burst blocking probabilities in an 8- channel network with a burst arrival rate of 30 transmissions per second. 6 Architecture Conventional CC-7DC ± Conventional 2CC-6DC ± Conventional 3CC-5DC ± Conventional 4CC-4DC ± Conventional 5CC-3DC ± Conventional 6CC-2DC ± Conventional 7CC-DC ± Shared Channel ± total number of channels on a link. Under these conditions, the conventional OBS architecture achieves its lowest burst blocking probability using two control channels (CCs) and six data channels (DCs). The proposed architecture is able to achieve the lowest overall burst blocking probability. Table indicates a fair, though not perfect, analysis of both the conventional and the proposed architectures. Our subsequent simulations will explore this accuracy further. 4.2 Effect of Load The results of the analysis and simulation for both the conventional and the proposed architecture under various loads in the network with eight channels per link and an average DB size of 40,000 bits are presented in Fig. 3. The simulation and analysis follow a very close trend, confirm- 8 0

6 ing our analysis as a reasonable model for the architectures under these conditions. The analysis results for the conventional architecture appear to be most accurate when there are between two to four control channels. Next we repeat the previous set of tests with sixteen channels instead of eight. The results are given in Fig. 4. From the figures, we observe that our analysis is quite accurate in reproducing the burst blocking probabilities obtained in the simulation. A similar performance pattern to that found using eight channels is seen here, where the most accurate analysis results for the conventional architecture occur when the number of control channels and data channels is not too large or small. Intuitively, when there is a small number of control channels the contribution to the total blocking probability due to the congestion in the control channels will be great. On the other hand, when there are few data channels and many control channels, the contribution due to congestion in the data channels will dominate the total blocking probability. It seems that the error of our analysis is the greatest when these individual contributions are at their highest. Even considering the error, our analysis still does a very reasonable job of approximating the simulation. In both 8 and 6 channel scenarios, we observe that the analysis results closely follow those of simulation for the proposed architecture. 4.3 Effect of DB Size Freezing the load at 5% and the total number of channels at eight, we vary the average DB size from 20,000 to 220,000 bits in this next experiment. Observing the results in Fig. 5, we find that increasing the average DB size only affects the blocking probabilities of the conventional architecture when there is only one control channel. In this case, the blocking probability reduces steadily since there are fewer BHPs generated for the same load as the average DB size increases. With two or more control channels, very little of the contribution to the blocking probability comes from BHPs. This is why there is no response to a variation in average DB size. We notice something interesting when observing the analysis and simulation results for the proposed architecture. At a DB size of 20,000 bits the blocking probability produced by the simulation actually exceeds that of the analysis. At 40,000 bits, they seem to cross over. At values above 40,000 bits, the analysis has a higher blocking probability. This seems to indicate that the analysis does not match as well when there are high numbers of BHPs as is the case with a DB size of 20,000 bits. If we had chosen any other value of DB size greater than 40,000, our analysis would be more pessimistic than the actual simulation results. The DB size, however, does not affect the overall standing of the proposed architecture since the conventional architecture is hardly affected by changes in DB size and the proposed architecture also encounters very little change. 5 Performance Results Now that we have seen that our analytic modeling is able to reproduce our simulation with reasonable accuracy, we will use our analysis to better understand the differences in performance between the two architectures. 5. Impact of Number of Channels In Fig. 6, we graph the results of our analysis for the conventional and the proposed architectures under various loads in the network with eight channels and an average DB size of 40,000 bits. The results of analysis for the proposed architecture reveals a lower blocking probability compared to that of the conventional architecture. The proposed architecture offers better system utilization by allowing more flexible channel allocation. Notice that under low loads, the conventional architecture configured with two control channels has a much lower blocking probability than that which uses only one. However, as the load increases, the conventional architecture with one control channel yields a lower blocking probability. Therefore, the best configuration of the conventional architecture varies depending on the traffic load. Even if a conventional architecture could achieve the best of all configurations by adjusting the number of control and data channels depending on the offered load, the proposed architecture would still offer the lowest blocking probability. Repeating this same test using the network with sixteen total channels shows a similar performance pattern. From Fig. 7, we observe that the proposed architecture exhibits the lowest overall blocking probability. The most ideal configuration for the conventional architecture is again dependent on the offered load. 5.2 Impact of DB Size In this set of tests, we vary the average size of DBs. Fig. 8 shows the results of varying the average DB size from 20,000 bits to 260,000 bits. Increasing the size of DBs affects how many BHPs are transmitted. For example, doubling the average DB size should produce half as many BHPs. The benefit of the proposed architecture decreases with the changes in the DB size initially. However, this decrease lessens in intensity as the size of the DB increases. The proposed architecture continues to offer an advantage despite these changes in the average DB size. The most ideal configuration of the conventional architecture depends on the average DB size used.

7 5.3 Impact of Total Number of Channels Overall Blocking -- Conventional -- CC - 7DC Another parameter that may affect the performance is the total number of channels used in the network. In Fig. 9, we show how both architectures perform in the network featuring from two to sixteen channels per link, an average DB size of 40,0000 bits, and a load of 5%. Again the proposed architecture maintains its advantage over the conventional architecture. The conventional architecture does well with one control channel until there are a total of seven channels. At this point, the conventional architecture is better off with two control channels. 6 Conclusions Overall Blocking -- Conventional -- 4CC - 4DC In this paper, we investigated a shared channel OBS architecture that allows the transfer of both burst header packets and data bursts on the same wavelength channel with some modifications on the conventional OBS architecture. Based on the reduced load fixed point approximation and assuming no BHP loss due to O/E/O contention, we provided an analytic model for burst blocking probability analysis under the proposed architecture which employs the just-enough-time signaling and fixed routing. The accuracy of the analytic model is validated via extensive simulation. Our analysis and simulation showed that the proposed architecture achieves a significantly lower burst blocking probability compared with the conventional architecture. We also showed that the best configuration of the conventional architecture depends on the load, average data burst size, and total number of channels. Therefore, the proposed architecture is easier to configure and achieves better overall performance. The tradeoffs between the O/E/O cost and system performance will be further studied in the future work Overall Blocking -- Conventional -- 7CC - DC References [] N. Calabretta. All-Optical Header Processing Based on Nonlinear Gain and Index Dynamics in Semiconductor Optical Amplifiers. Ph.D. Dissertation, Faculty of Electrical Engineering, Eindhoven University of Technology, [2] X. Cao, J. Li, Y. Chen, and C. Qiao. Assembling TCP/IP Packets in Optical Burst Switched Networks, [3] L. Y. Chan and et al. All-Optical Header Processing Using an Injection-locked Fabry-Perot Laser Diode. Microwave and Optical Technology Letters, 44(4): , February [4] Y. Chen, H. Wu, D. Xu, and C. Qiao. Performance analysis of optical burst switched node with deflection routing. IEEE International Conference on Communications (ICC), Ankerage, Ak, 2: , e-04 Overall Blocking -- Shared Channel e Figure 3. Validation of analytic model: burst blocking probabilities versus offered network load in a network with 8 channels, variable number of control channels, and 40,000 bits average DB size.

8 Overall Blocking -- Conventional -- CC - 5DC Overall Blocking -- Conventional -- CC - 7DC Average DB Size (Bits) Overall Blocking -- Conventional -- 8CC - 8DC Overall Blocking -- Conventional -- 4CC - 4DC Average DB Size (Bits) Overall Blocking -- Conventional -- 5CC - DC Overall Blocking -- Conventional -- 7CC - DC Average DB Size (Bits) Overall Blocking -- Shared Channel Overall Blocking -- Shared Channel e-04 e-05 e-06 e-07 e-08 e Average DB Size (Bits) Figure 4. Validation of analytic model: burst blocking probabilities versus offered network load in a network with 6 channels, variable number of control channels, and 40,000 bits average DB size. Figure 5. Validation of analytic model: burst blocking probabilities versus average DB size in a network with 8 channels, variable number of control channels, and 5% load.

9 Overall Blocking -- Conventional vs. Shared Channel -- Overall Blocking -- Conventional vs. Shared Channel CC - 7DC -- Conventional 2CC - 6DC -- Conventional e-04 3CC - 5DC -- Conventional 4CC - 4DC -- Conventional 5CC - 3DC -- Conventional 6CC - 2DC -- Conventional 7CC - DC -- Conventional Shared Channel e CC - 7DC -- Conventional 2CC - 6DC -- Conventional 3CC - 5DC -- Conventional 4CC - 4DC -- Conventional 5CC - 3DC -- Conventional 6CC - 2DC -- Conventional 7CC - DC -- Conventional Shared Channel Average DB Size (Bits) Figure 6. Performance comparison between conventional architecture and shared architecture: burst blocking probabilities versus offered load in a network with 8 channels and 40,000 bits average DB size. Figure 8. Performance comparison between conventional architecture and shared channel architecture: burst blocking probabilities versus average DB size in a network with 8 channels and 5% load. Overall Blocking -- Conventional vs. Shared Channel -- Variable Number of Channels (2-6) e-04 e-05 e-06 CC - 5DC Conventional 3CC - 3DC Conventional e-07 5CC - DC Conventional 7CC - 9DC Conventional 9CC - 7DC Conventional e-08 CC - 5DC Conventional 3CC - 3DC Conventional 5CC - DC Conventional Shared Channel e cc Conventional 2cc Conventional 3cc Conventional 4cc Conventional 5cc Conventional 6cc Conventional 0.07cc Conventional 8cc Conventional 9cc Conventional 0cc Conventional cc Conventional 2cc Conventional 3cc Conventional 4cc Conventional 5cc Conventional Shared Channel Total Number of Channels Figure 7. Performance comparison between conventional architecture and shared channel architecture: burst blocking probabilities versus offered load in a network with 6 channels and 40,000 bits average DB size. Figure 9. Performance comparison between conventional architecture and shared channel architecture: burst blocking probabilities versus total number of channels in a network and 40,000 average DB size.

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