Photonic Network Communications

, Volume 31, Issue 3, pp 457–465 | Cite as

Performance analysis and transmission strategies comparison for synchronous WDM passive star LANs

Article

Abstract

Two synchronous transmission strategies suitable for optical WDM networks of passive star topology are presented in this study. The fiber bandwidth is divided into parallel WDM channels: the control and the data channels, while the number of control channels is less than the number of data channels. In particular, the control channels are used for the control information exchange prior to the data packet transmission, aiming to avoid the data channel collisions. This is achieved by effectively exploiting the propagation delay latency as appropriate acknowledgment time. The first transmission strategy performs the data channel collisions avoidance by allowing only one station per cycle to transmit over a data channel, employing appropriate transmission rules, like in [12]. On the other hand, the second transmission strategy (Improved Protocol) assigns to each control channel a dedicated data channel to ensure that each successfully transmitted control packet corresponds to a successful data packet transmission. Thus, it requires less processing overhead as compared to the first one. The performance of both the WDMA strategies are analytically studied based on Markovian models for finite population, while the performance measures are derived by closed mathematical formulas. The protocol performance is extensively studied for various number of stations, control and data channels. Finally, the comparison of the two protocols proves that second one essentially improves the throughput, while this improvement is an increasing function of the number of control channels.

Keywords

Collisions avoidance Propagation delay latency Wavelength division multiplexing 

1 Introduction

Nowadays optical networks mostly employ the wavelength division multiplexing (WDM) [1] technique to effectively divide the huge fiber bandwidth into parallel channels, each operating in lower data rate. A WDM network performance is mainly depended on the WDM access (WDMA) strategy followed. Some WDMA protocols that have been proposed in the literature assume random channel access, like in [2]. It is obvious that they suffer from packet collisions over the control and data channels, providing performance deterioration. Thus, pre-transmission coordination WDMA protocols have been proposed in order to provide appropriate transmission rules for the data channel collisions avoidance. Key role on the pre-transmission WDMA protocols performance undoubtedly plays the propagation delay parameter, since it can be exploited as the required acknowledgment time in order for the control information to be exchanged and the transmission coordination rules to be followed.

Despite the critical impact on the network efficiency of the round trip propagation delay as it is compared with the data packet transmission time, few studies take it under consideration. For example, for a passive star WDM network, the propagation delay between the stations and the hub is used for the data transmissions schedule, like in [3]. A collision-free pre-transmission coordination protocol that predicts the transmission requests from all the stations and reduces the scheduling time is given in [4]. Finally, in [5] the propagation delay is exploited to schedule the transmissions and derive the performance measures of two reservation-based WDMA protocols.

In the literature, many WDMA protocols of passive star topology that use a single control channel to exchange control information prior to the data packet transmission are presented [2, 6, 7, 8]. In these protocols, the adopted access algorithms that take into account the control information achieve significant performance improvement, although they introduce electronic processing bottleneck [9]. In other words, the use of a single control channel limits the reception and the processing of the exchanged control information to the processing rate of the electronic interfaces. Thus, the multi-channel control architecture (MCA) that employs a number of control channels for control information exchange has been proposed [10, 11]. In particular, the MCA provides less control information processing overhead, since it is distributed on a set of control channels and is processed in a parallel way, giving performance improvement.

In this paper, two pre-transmission access strategies suitable for slotted passive star WDM local area networks (LANs) are presented. The MCA use to exchange control information prior to the data packets transmission effectively faces the data channel collisions. In both access strategies, the round trip propagation delay is assumed to be longer than the data packet transmission time. This attribute is exploited as acknowledgment time period during which the control information is exchanged and after the end of which collision-free data packet transmissions can be scheduled.

Particularly, the first access strategy is referred as data channel collisions avoidance (DCCA) protocol and adopts a simple access algorithm according to which each station selects in a random way the control channel for control information transmission, while proper arbitration rules are utilized to avoid possible collisions over the data channels. Part of this protocol has been studied in [12]. On the contrary, the second access strategy that is referred as Improved Protocol achieves to totally avoid the data channel collisions based on the improved control information exchanged over the MCA. In other words, the control packets that are exchanged during the pre-transmission phase include the proper control information that ensures the successful data packet transmission over the data channel system. Thus, the Improved Protocol provides less processing overhead since it manages the data channel collisions avoidance in a simpler way, while it achieves significant throughput improvement under high offered load conditions for various number of control channels.

In both WDMA strategies, it is assumed that the number of control channels in the MCA is less than the number of data channels. This fact provides a less costly implementation, since the required number of fixed receivers per station is less, as compared to the studies of [10, 11].

For each WDMA strategy, a Markovian model for finite station population is developed while the performance measures are estimated by means of closed analytical formulas. Extensive performance study is provided for various numbers of control channels, data channels and nodes population. Finally, comparative study between the two WDMA strategies is given for diverse numbers of control channels in the MCA.

This work is carried out as follows: Sect. 2 describes the network model and the assumptions. In Sects. 3 and 4, the DCCA and the Improved Protocols are studied, respectively. For each protocol, the Markovian model is analyzed, the performance measures are analytically derived, and the performance evaluation is given, while the comparison is studied. Finally, Sect. 5 outlines some conclusions.

2 Network model and assumptions

In Fig. 1, the assumed passive star network model is illustrated. The system uses \(v+N\,(v<N)\) wavelengths \(\lambda _{c1},\ldots ,\lambda _{cv},\lambda _{d1},\ldots ,\lambda _{dN}\) to serve a finite number M of stations. The multi-channel system at wavelengths \(\lambda _{c1},\ldots ,\lambda _{cv}\) forms the MCA, while the remaining N channels at wavelengths \(\lambda _{d1},\ldots ,\lambda _{dN}\) constitute the data multi-channel system. In other words, there are v control channels and each station has a tunable transmitter that can be tuned to a wavelength in the set \(\lambda _{c1},\ldots ,\lambda _{cv},\lambda _{d1},\ldots ,\lambda _{dN}\). The outcoming traffic of a station is connected to an input of the passive star coupler. Each station uses v fixed receivers one for each control channel and one tunable receiver to any of data channels \(\lambda _{d1},\ldots ,\lambda _{dN}\). The incoming traffic to a station is split into \(v+1\) portions by an \(1\times (v+1)\) WDMA splitter, as Fig. 1 shows.

The transmission time of a fixed size control packet is used as time unit, and the data packet transmission time normalized in time units is L (data slot). The normalized round trip propagation time between any station to the star coupler hub and to any other station is equal to R data slots (\(R\times L\) time units) for all stations.
Fig. 1

Network architecture

Fig. 2

Cycle definition

Both control and data channels use the same time reference which we call cycle. We define as cycle C the time interval that includes one time unit for control packet transmissions plus the normalized round trip propagation time \(R\times L\), plus the data packet transmission time L. Thus, the cycle time duration C is defined as:
$$\begin{aligned} C=1+\left( {R+1}\right) \times \hbox {L time units} \end{aligned}$$
(1)
The cycle time duration C is presented in Fig. 2.

We assume a common clock to all stations. Time axis is divided into contiguous cycles of equal length, and stations are synchronized for transmission on the control and data channels during a cycle. At any point in time each station is able to transmit at a given wavelength \(\lambda _\mathrm{T}\) and simultaneously to receive at a wavelength \(\lambda _\mathrm{R}\). For the tunable transceivers, we assume negligible tuning times and very large tunable ranges.

Each station is equipped with a transmitter buffer with capacity of one data packet. If the buffer is empty, the station is said to be free, otherwise it is backlogged. Packets are generated independently at each station following a geometric distribution; i.e., a packet is generated at each cycle with probability p. A backlogged station retransmits the unsuccessfully transmitted packet following a geometric distribution with probability \(p_{1}\) and defers the transmission by one cycle with probability \((1-p_{1})\). If a station is backlogged and generates a new packet, the packet is lost.

3 Data channel collisions avoidance (DCCA) WDMA protocol

In the DCCA protocol, we assume that the control packet includes information about: the source address, the destination address, and the data wavelength \(\lambda _{k}\) that belongs to the set of \(\lambda _{d1},\ldots ,\lambda _{dN}\) and has been chosen by the source for the data packet transmission.

3.1 Transmission and reception mode

At the beginning of each cycle if a station has to send a data packet to another station, it first chooses randomly a data channel on which the packet will be transmitted. Then, it informs the other stations by sending a control packet over the MCA, choosing randomly one of the v control channels. The control packets compete according to the Slotted Aloha scheme to gain access. The station continuously monitors the MCA with its fixed receivers. The outcome of its control packet will be known \(R\times L\) time units later (acknowledgment period of time) because of the broadcast nature of the control channels. After the end of this period, the station is informed about the control packets that have been successfully transmitted. In particular, if its control packet has been successfully transmitted over the MCA and the same data channel has been also selected from some other stations for data transmission, a data channel collisions avoidance algorithm is applied (we can imagine several arbitration rules, as the packet age, the priority, etc). In this case, only one among the competed for the same data channel stations gains access and starts immediately transmission, while the others are getting backlogged.

After the data packet transmission, the destination station waits \(R\times L\) time units, while the data packet is transmitted from the source to the destination. Then, it adjusts its tunable receiver to the data channel specified in the control packet for reception.

Free stations that unsuccessfully transmit on the control channels or their data channel transmission is canceled due to data channel collisions during a cycle are getting backlogged on the next cycle. A backlogged station is getting free at the next cycle if it manages to retransmit without collision over a control channel and to gain access over a data channel.

3.2 Performance analysis

The system is described by a discrete time Markov chain. We denote the system state by \(X_{t}\), \(t=1,2,\ldots \) where \(X_{t}=0,1,\ldots ,M\) is the number of backlogged stations at the beginning of a cycle and t denotes the time that continuously increases. Let:

\(H_{t}=\) The number of new control packet arrivals at the first control slot of a cycle, \(t=0,1,2,\ldots \)

\(A_{t}=\) The number of successfully (re)transmitted data packets over the N data channels during a cycle, \(t=0,1,2,\ldots \)

\(S_{k}=\) The number of successful control packet (re)transmissions over the v control channels, conditional that k free and/or backlogged stations attempt transmission during a cycle, and \(0\le Sk\le \min (v,k)\).

\(A_{n}=\) The number of successful data packet (re)transmissions over the N data channels, conditional that n successful (re)transmissions occurred over the v control channels during a cycle, \(S_{k}=n\) for every \(S_{k}>0\).

The probability \(\Pr [S_{k}=n]\) of n successes from k transmissions on the v control channels during a cycle is [13]:
$$\begin{aligned} \Pr [S_k=n]=\frac{(-1)^{n}v!k!}{v^{k}n!}\sum _{j=n}^{\min (v,k)} {\frac{(-1)^{j}(v-j)^{(k-j)}}{(j-n)!(v-j)!(k-j)!}}\nonumber \\ \end{aligned}$$
(2)
and \(0\le n\le \min (v,k)\).
The probability \(\Pr [A_{n}=r]\) of r successful transmissions on the N data channels given that n successful (re)transmissions occurred over the v control channels during a cycle is [14]:
$$\begin{aligned} \Pr [A_n =r]=\left( {{\begin{array}{l} N \\ r \\ \end{array} }} \right) \sum _{i=0}^r {(-1)^{i}\left( {{\begin{array}{l} r \\ i \\ \end{array} }} \right) \left( {\frac{r-i}{N}} \right) ^{n}} \end{aligned}$$
(3)
and \(1\le r\le \min (N,n)\) for every \(n\ge 1\).
The function \(\varPhi (x,y,z)\) is defined as the product of the probability of y successes from x transmissions on the v control channels, times the probability of z successfully transmitted packets on the N data channels during a cycle:
$$\begin{aligned} \varPhi (x,y,z)=\Pr [S_x=y]\Pr [A_y=z] \end{aligned}$$
(4)
Also, we define the conditional probability \(q_{in}\) that i out of n backlogged stations attempt to retransmit with probability \(p_{1}\) during the cycle. \(q_{in}\) is given by:
$$\begin{aligned} q_{in}=\hbox {bin}(n,i,p_1) \end{aligned}$$
(5)
Similarly, the conditional probability \(Q_{in}\) that i out of \((M-n)\) free stations attempts to transmit with probability p during the cycle is defined as:
$$\begin{aligned} Q_{in}=\hbox {bin}(M-n,i,p) \end{aligned}$$
(6)
where
$$\begin{aligned} \hbox {bin}(i,j,p)=\left( {{\begin{array}{l} i \\ j \\ \end{array} }} \right) p^{j}(1-p)^{i-j},\quad i\ge j \end{aligned}$$
(7)
The Markov chain \(X_{t}\,t=1,2,\ldots \) is homogeneous, aperiodic and irreducible. The one step transition probabilities are given by: \(P_{ij}=(X_{t+1}=j\vert X_{t}=i\)), where:
If: \(j<i-v\), then:
$$\begin{aligned} P_{ij} =0 \end{aligned}$$
(8)
If: \(j=i-v\), then:
$$\begin{aligned} P_{ij} =q_{vi} Q_{0i} \varPhi (v,v,v) \end{aligned}$$
(9)
If: \(i-v<j<i\), then:
$$\begin{aligned} P_{ij} =\left\{ \begin{array}{l} \sum \limits _{n=i-j}^{\min (i,v)} q_{ni} \sum \limits _{m=0}^{\min (v-n,M-i)}Q_{mi} \varPhi (n +m,n+m,\\ \quad m+i-j) + \sum \limits _{n=i-j+2}^i {q_{ni} } \sum \limits _{m=0}^{\min (v-i+j-1,M-i)} \\ \quad \times Q_{mi} \sum \limits _{s=m+i-j}^{\min (n+m-2,v-1)} {\varPhi (n+m,s,m+i-j)} \\ \end{array} \right. \end{aligned}$$
(10)
If: \(j=i\), then:
$$\begin{aligned} P_{ij} =\left\{ {{\begin{array}{l} Q_{0i} \sum \limits _{n=2}^i {q_{ni} \varPhi (n,0,0)} + q_{0i} \sum \limits _{m=0}^{\min (M-i,v)}\\ \quad \times {Q_{mi} \varPhi (m,m,m)} + \sum \limits _{n=1}^{\min (i,v)} q_{ni} \sum \limits _{m=1}^{\min (M-i,v-n)}\\ \quad \times {Q_{mi} \varPhi (n+m,n+m,m)} + \sum \limits _{n=1}^i q_{ni} \\ \quad \times \sum \limits _{m=1}^{\min (M-i,v-1)} Q_{mi} \sum \limits _{s=m}^{\min (n+m-2,v-1)}\\ \quad \times {\varPhi (n+m,s,m)} \\ \end{array} }} \right. \end{aligned}$$
(11)
If: \(j>i\), then:
$$\begin{aligned} P_{ij} =\left\{ {{\begin{array}{l} {Q_{j-i,i} \sum \limits _{n=0}^i {q_{ni} \varPhi (n+j-i,0,0)}} \\ \quad +\,\sum \limits _{n=0}^{\min (i,v)} {q_{ni} } \sum \limits _{m=j-i+1}^{\min (M-i,v-n)} Q_{mi} \varPhi (n+m, \\ \quad n+m,m+i-j) + \sum \limits _{n=0}^i q_{ni} \\ \quad \times \sum \limits _{m=j-i+1}^{\min (M-i,v-i+j-1)}\\ \quad \times {Q_{mi} } \sum \limits _{s=m+i-j}^{\min (n+m-2,v-1)} {\varPhi (n+m,s,m+i-j)} \\ \end{array} }} \right. \end{aligned}$$
(12)
Since the Markov chain \(X_{t}\), \(t=1,2,\ldots \) is ergodic, the steady-state probabilities are given by solving the system of the following linear equations:
$$\begin{aligned} \pi =\pi \,P \end{aligned}$$
(13)
and
$$\begin{aligned} \sum _{i=0}^M {\pi _i =1} \end{aligned}$$
(14)
where P is the transition matrix with elements, the probabilities \(P_{ij}\), and \(\pi \) is a row vector with elements, the steady-state probabilities \(\pi _{i}\).
The conditional throughput S(i) is the expected value of the output rate during a cycle conditional that the number of backlogged stations at the beginning of the cycle is i; i.e., \(S(i)=E[A_{t}\vert X_{t}=i]\) and is given by:The steady-state average throughput S is given by:
$$\begin{aligned} S=\frac{L}{C}E[S(i)]=\frac{L}{C}\sum _{i=0}^M {S(i)\pi _i } \end{aligned}$$
(16)
The steady-state average number B of backlogged stations is:
$$\begin{aligned} B=E[i]=\sum _{i=0}^M {i\pi _i } \end{aligned}$$
(17)
The conditional input rate \(S_{in}(i)\) is the expected number of arrivals during a cycle, given that the number of backlogged stations at the beginning of a cycle is i. It is:
$$\begin{aligned} S_{in} (i)=E[H_t |X_t =i]=(M-i)p \end{aligned}$$
(18)
The steady-state average input rate \(S_{in}\) is given by:
$$\begin{aligned} S_{in} =\sum _{i=0}^M {p(M-i)\pi _i } \end{aligned}$$
(19)
The delay D is defined as the average number of time units that a data packet has to wait until its successful transmission. It is:
$$\begin{aligned} D=\{1+(R+1)L\}+\{1+(R+1)L\}\frac{B}{S_{in} } \end{aligned}$$
(20)
Finally, we define the throughput per data channel \(S_{d}\) in steady state as the number of the successfully transmitted data packets per data channel during a cycle. It is:
$$\begin{aligned} S_d =\frac{S}{N}. \end{aligned}$$
(21)

3.3 Performance evaluation

In the followings, we assume that the data packet length is: \(L=10\) time units. In order to validate the accuracy of the proposed protocol analysis, we developed a simulation program that simulates the proposed protocol performance. As it is shown in Fig. 3, the simulation results have one-to-one correspondence to the analytical ones.
Fig. 3

D versus \(S_{d}\), for \(M=50\), \(N=30\), \(R=5\), and \(v=10, 15,20\). Analysis and simulation

Figure 3 shows the delay D curves versus the throughput per data channel \(S_{d}\), for \(M=50\), \(N=30\), \(R=5\), and \(v=10,15,20\). It is observed that for fixed values of M, N, and R, the maximum value of \(S_{d}\) rises as v increases. This is because as v grows, the number of control channel collisions reduces. Consequently, this fact gives rise to the data packet transmission probability over the data channels, as a direct result of the employment of the data channel collisions avoidance algorithm. It is evident that as v increases, the entire protocol performance improves reaching significant higher throughput and considerable lower delay, as Fig. 3 depicts. This is a direct result of the bandwidth utilization improvement provided. For example, the maximum \(S_{d}\) value increases about 65 % if we use \(v=15\) instead of \(v=10\) and 112 % if we use \(v=20\) instead of \(v=10\) control channels.

On the other hand, Fig. 4 depicts the delay D curves versus the throughput per data channel \(S_{d}\), for \(M=50\), \(v=10\), \(R=5\), \(N=30, 40, 50\). As N increases, the probability of a data packet successful transmission over the data multi-channel system increases too. This fact causes the \(S_{d}\) decrease as (21) ensures. For example, the maximum \(S_{d}\) value decreases: 12 % if we use \(N=40\) instead of \(N=30\) and 41 % if we use \(N=50\) instead of \(N=30\) stations. Also, it is remarkable that as N increases the number of backlogged stations B increases too, due to the decrease in the \(S_{d}\) values. This fact causes the significant increase in D with the N increment, as Fig. 4 illustrates and (20) validates.
Fig. 4

D versus \(S_{d}\), for \(M=50\), \(v=10\), \(R=5\), \(N=30,40,50\)

Fig. 5

\(S_{d}\) versus p, for \(N=30\), \(v=10\), \(R=5\), and \(M=50, 75,100\)

The impact of the number M variation on the system performance is presented in Fig. 5 that presents the throughput per data channel \(S_{d}\) curves versus the birth probability p, for \(N=30\), \(v=10\), \(R=5\), and \(M=50,75,100\). It is noticed that as M increases, the \(S_{d}\) decreases. This is because, as M increases for fixed NvR and p, the probability of control and data channel collisions significantly increases. This fact results to the throughput per data channel decrease. This behavior is observed for example, for \(p=0.9\) where \(S_{d}\) decreases: 35 % if we use \(M=75\) instead of \(M=50\) and 59 % if we use \(M=100\) instead of \(M=50\).

Finally, the variation of the normalized round trip propagation delay latency R parameter is studied in Fig. 6. In particular, Fig. 6 illustrates the delay D curves versus the throughput per data channel \(S_{d}\), for \(M=50\), \(N=30\), \(v=10\), and \(R=0,5,10\). As it is observed, the impact of the R on the protocol performance is critical, and for this reason, it should be taken into account to the WDMA protocol evaluation. For example, in case that we ignore the R impact, i.e., for \(R=0\), the protocol seems to reach high throughput and low delay. This result is not true in real conditions. As it is studied for \(R=5,10\), the performance obtained in a decreasing function of R. In other words, as R increases the maximum throughput decreases. This result conforms to that of (16) and (21), since the cycle duration increases according to (1). Also, as R increases the delay obtained rises, as (20) verifies.
Fig. 6

D versus \(S_{d}\), for \(M=50\), \(N=30\), \(v=10\), \(R=0,5,10\)

4 Improved WDMA protocol

In the Improved Protocol, we assume that for each control channel in the MCA a specific data channel is assigned to it. Also, we consider that the control packet includes information about: the source address and the destination address of the relative data packet.

4.1 Transmission and reception mode

At the beginning of each cycle, if a station has to send a data packet to another station, it chooses randomly one of the v a control channels over which it sends a control packet in order to inform the other stations for its attempt. The control packets compete according to the Slotted Aloha scheme, as in the DCCA protocol. The outcome of its control packet transmission will be known \(R\times L\) time units later. If its control packet has been successfully transmitted, the station starts immediate data packet transmission over the corresponding data channel that is assigned to the chosen control channel. After the data packet transmission, the destination station waits \(R\times L\) time units while the data packet is transmitted from the source to the destination. Then, it adjusts its tunable receiver to the corresponding data channel for reception.

Free stations that unsuccessfully transmit on the control channels during a cycle are getting backlogged on the next cycle. A backlogged station is getting free at the next cycle if it manages to retransmit without collision over a control channel.

4.2 Performance analysis

As in the DCCA protocol, the system is described by a discrete time Markov chain. We assume the random variables: \(X_{t}\), \(H_{t}\), \(A_{t}\), and \(S_{k}\), as in Sect. 3.2.

The probability \(\Pr [S_{k}=n]\) of n successes from k transmissions on the v control channels during a cycle is given by (2).

Based on the results of [13], we derive the one step transition probabilities \(P_{ij}=(X_{t}+1=j\vert X_{t}=i\)), where:

If: \(j<i-v\), then:
$$\begin{aligned} P_{ij} =0 \end{aligned}$$
(22)
If: \(j=i-v\), then:
$$\begin{aligned} P_{ij} =q_{vi} (1-p)^{(M-j-v)}\Pr [S_v ,v] \end{aligned}$$
(23)
If: \(j=i-1\), then:
$$\begin{aligned} P_{ij}=\sum _{n=0}^M {\sum _{s=0}^{\min (v,n)} {q_{(n-s+1)i} Q_{(s-1)i} \Pr [S_n ,s]} } \end{aligned}$$
(24)
If: \(j=i\), then:
$$\begin{aligned} P_{ij} =\sum _{n=0}^M {\sum _{s=0}^{\min (v,n)} {q_{(n-s)i} Q_{si}\Pr [S_n ,s]} } \end{aligned}$$
(25)
If: \(j=i+1\), then:
$$\begin{aligned} P_{ij}=\sum _{n=0}^M {\sum _{s=0}^{\min (v,n)} {q_{(n-s-1)i} Q_{(s+1)i} \Pr [S_n ,s]} } \end{aligned}$$
(26)
If: \(j>i-v\), then:
$$\begin{aligned} P_{ij}=\sum _{n=0}^M {\sum _{s=0}^{\min (v,n)} {q_{(n-j+i-s)i} Q_{(j-i+s)i} \Pr [S_n ,s]} } \end{aligned}$$
(27)
The conditional throughput is:
$$\begin{aligned} S(i)= & {} \sum _{n=0}^M {\left( {\sum _{s=0}^{\min (v,n)} {s\Pr [S_n ,s]} } \right) } \nonumber \\&\times \left( {\sum _{j=\max (0,n-i)}^{\min (n,M-i)} {q_{(n-j)i} Q_{ji} } } \right) \end{aligned}$$
(28)
The average throughput S, the average number B of backlogged stations, the average input rate \(S_{in}\), the delay D, and the throughput per data channel \(S_{d}\) are given by (16), (17), (19), (20), and (21), respectively.

4.3 Performance evaluation and comparison

In the following, we assume that \(L=10\) time units. Figure 7 depicts the throughput per data channel \(S_{d}\) curves versus the birth probability p, for \(M=30\), \(N=30\), \(R=5\), and \(v=10,15,20\) for the Improved Protocol comparatively to the DCCA one. Also, Fig. 8 shows the delay D curves versus the throughput per data channel \(S_{d}\), for \(M=30\), \(N=30\), \(R=5\), and \(v=10,15,20\) for the Improved Protocol comparatively to the DCCA one.
Fig. 7

\(S_{d}\) versus p, for \(N=30\), \(M=30\), \(R=5\), and \(v=10,15,20\)

Fig. 8

D versus \(S_{d}\), for \(N=30\), \(M=30\), \(R=5\), and \(v=10,15,20\)

As Fig. 7 depicts for the Improved Protocol, for fixed values of M, N, R, and p, the \(S_{d}\) rises as v increases. This is due to the fact that as v is getting higher, the number of control channel collisions and backlogged stations is getting lower. Subsequently, this fact gives rise to the data packet transmission probability over the data channels, as a direct result of the data channels one to one correspondence to the control channels. For example, for \(p=0.9\), the \(S_{d}\) is: 0.015 data packets/cycle for \(v=10,0.03\) data packets cycle for \(v=15\), and 0.037 data packets/cycle for \(v=20\). This behavior is validated in Fig. 8. As it is representatively shown, the performance improvement is an increasing function of v. This result is based on the above discussion.

Finally, the comparative study between the DCCA and the Improved Protocol proves the advantages of the second one. Indeed, as Fig. 7 presents for fixed values of M, N, R, and p the \(S_{d}\) value of the Improved Protocol is higher than that of the DCCA one. This is understood since the Improved Protocol totally faces the data channel collisions by assigning a data channel to each control channel. This means that the Improved Protocol ensures that each station which has successfully transmitted over the MCA is able to successfully transmit over the data channels. This assurance is not valid in the DCCA protocol. This is because, according to the applied data channel collisions avoidance algorithm, if more than one successfully transmitted packets over the MCA compete for the same data channel only one of them gains access while the others are aborted. For this reason, for the DCCA protocol the average number of backlogged stations during a cycle is higher than the relative number of the Improved one, providing lower \(S_{d}\) value under the same load conditions. As an immediate result, the \(S_{d}\) enhancement that the Improved Protocol provides in an increasing function of v. For example, for \(p=0.9\), the \(S_{d}\) increases about 5.3 % for \(v=10\), 7.2 % for \(v=15\), and 14.7 % for \(v=20\).

5 Conclusion

In this paper, we present two synchronous transmission WDMA protocols for passive star topology that exploit the round trip propagation delay latency as acknowledgment time to adopt proper data channel collisions avoidance algorithms. The first protocol, called DCCA protocol, effectively faces the data channel collisions by imposing only one data packet transmission per data channel during a cycle, rejecting all the other competed packets, and providing extra possible packet loss. The second one, called Improved Protocol, assigns to each control channel a data one, ensuring that there are no data channel collisions and packet loss. For this reason, the Improved Protocol provides essential performance improvement as compared to the DCCA one, for various number of control channels. The powerful advantage of the second protocol is that the performance improvement achieved does not imply any additional cost or complexity. On the contrary, it is managed by properly exploiting suitable additional control information that is exchanged among the stations at the pre-transmission reservation phase. Finally, it has been proven that this performance improvement is an increasing function of the control channels.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece

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