Modeling Telecommunication Infrastructures Integrating Wideband

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Modeling Telecommunication Infrastructures Integrating Wideband Wireless and Wired Networks Paolo Arseni, Gennaro Boggia and Pietro Camarda SIMULATION 2002; 78; 173 DOI: 10.1177/0037549702078003528 The online version of this article can be found at: http://sim.sagepub.com/cgi/content/abstract/78/3/173

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Modeling Telecommunication Infrastructures Integrating Wideband Wireless and Wired Networks Paolo Arseni Gennaro Boggia Pietro Camarda† Dipartimento di Elettrotecnica ed Elettronica Politecnico di Bari, 70125 Bari, Italy [email protected] Future telecommunication systems will integrate wireline and wireless networks in a single, advanced infrastructure. It is expected that such systems, in the wireless part, will exploit microcellular architectures in order to guarantee wideband multimedia services and to sustain the continuous growth of subscribers. In such a context, asynchronous transfer mode and Internet protocol are the basic technologies being considered by several studies and field implementations. In both cases, particular care has been devoted to cope with a large number of handoffs. This article considers some aspects of this integrated telecommunication infrastructure, proposing an improvement, for the wired part, of the virtual connection tree and shadow cluster concepts, whereas for the wireless part, a new model for the analysis of a dynamic channel allocation scheme is presented. The obtained analytical results, confirmed by simulation in a wide range of load conditions and user mobility, allow one to evaluate the main system performance parameters in terms of blocking probability of new calls, handoff-blocking probability, and forced termination probability. Keywords: Wireless asynchronous transfer mode (ATM), performance evaluation, mobility model, dynamic channel allocation

1. Introduction In the field of telecommunication, we are witnessing the impetuous evolution and expansion of two kinds of systems. The first is the universal wireline network that is now able to provide sophisticated multimedia services. The second comprehends the cellular network and is able to satisfy user mobility demand, providing standard telephone services and low-speed data transmission. On the horizon looms the project of a complete integration of wireline and wireless networks in a single, advanced infrastructure. The target is to obtain a complete integration of the telecommunication networks, at the same time guaranteeing complete mobility without any practical limitation in the available services. To optimize the utilization of spectral resources for the wireless part of such networks, it is necessary to employ microcellular architectures. In fact, the reduction of cell size appears to be the main tool to obtain high transmission capacities (spatial reuse of communication resources), indispensable to support wideband Submission Date: May 2001 Accepted Date: December 2001 † To whom all correspondence should be addressed.

SIMULATION, Vol. 78, Issue 3, March 2002 173-184 © 2002 The Society for Modeling and Simulation International

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multimedia services and to sustain the continuous growth of subscribers. On the other hand, microcellular architectures cause a large number of handoffs (i.e., a change of the cell of a user with a call in progress) that, generally, are a source of performance degradation. Each handoff process involves various control functions on the wired and wireless networks. Such control procedures, necessary to set up a connection with the new base station, introduce delay in the transmission, with catastrophic consequences in the case of multimedia real-time traffic. The design and implementation of such an integrated architecture, able to satisfy a large number of users with different service profiles, represent a challenging task. Several studies and field implementations are proposing solutions that consider either asynchronous transfer mode (ATM) or Internet protocol (IP) as basic technologies. In particular, ATM allows the simultaneous transmission of signals with different bandwidth requirements and quality of service (QoS) [1-6], whereas IP is more suited for integration with the existing, huge Internet world [7, 8]. In both cases, particular care must be devoted to the fast handoff problem created by the large number of microcell transitions by relatively fast mobile users. In this article, some aspects of this integrated telecommunication infrastructure are presented and analyzed


P. Arseni, G. Boggia, and P. Camarda

through analytical and simulation models. The wired network employs architectural solutions based on virtual connection tree (VCT) [1, 2] and shadow cluster [9] or, alternatively, on macro diversity or equivalent concepts [7, 8]. The wireless network adopts a dynamic channel allocation scheme [10-17]. The developed model, based on queueing networks, considers a finite number of users moving in a geographical region covered by a finite number of cells. The results allow us to evaluate the main system performance parameters in terms of blocking probability of new calls, handoff-blocking probability, and forced termination probability as a function of load and user mobility. 2. Network Architecture

Figure 1. Virtual connection tree

The utilization of the micro/picocellular architectures on future wireless systems introduces new problems. One of the most important is the increase of the intercell handoff rate. Each time a user transits to a new cell, during the same call, on the basis of the application’s specific parameters, one must evaluate the possibility of setting up a radio connection between the user and the new base station in addition to a wired connection to the base station of the destination. To execute this phase, the intervention of the network controller is necessary in order to establish the best route with the required quality of service. Therefore, each handoff process requires a large number of control functions on the wired network and on the wireless network. In this section, new architectural solutions are presented aimed at simplifying the handoff process. The basic principle is to optimize the service offered to mobile users exploiting the relatively large resources available in the wired network. 2.1 Virtual Connection Tree A new network architecture, proposed in [1, 2], is particularly suited for microcellular wireless ATM networks. In this model, the cells are clustered in sets denoting neighboring mobile access points, each of which constitutes the plant of a VCT. Such a VCT is a subsystem composed of a set of contiguous base stations, links of the wired network, switching units, and a control unit inside an ATM switch. All base stations belonging to the same VCT are interconnected by physical links and switching nodes. The connections are organized following a tree structure whose root is represented by the control unit, the branches by the wired links, and the leaves by the base stations (Fig. 1). The initialization procedure of a new call (at the wired network level) is carried out in two phases. The first consists of setting up the virtual connection between the root of the sender VCT and the root of the receiver VCT. In the second phase, the connections inside the involved VCT are set up, assigning a virtual connection between the root of the VCT and each base station of the corresponding tree.

When a user transits to a different cell of the same VCT, the handoff procedure is extremely fast and consists essentially of using a different virtual channel identifier, without the intervention of the admission controller. It can happen that a fast mobile user, moving from one cell to another during a call, reaches a cell belonging to a different VCT. This event, defined as VCT handoff, requires a slow procedure of admission control to initialize the new VCT, which usually is not compatible with the requirements of multimedia traffic. As a consequence, the necessity arises of limiting as far as possible the VCT handoffs, which can be obtained by enlarging, for fast users, the dimension of the tree that forms the VCT at the expense of wired network resources. Another problem that can arise with this approach is that during handoff, cell sequence cannot be maintained due to nonnegligible propagation time [3]. However, such a problem can be avoided by implementing a soft handoff mechanism as planned in third-generation cellular systems [8]. 2.2 Shadow Cluster The shadow cluster technique [9], which can be implemented over the VCT, is a predictive resource allocation scheme exploited to guarantee the QoS requested by a wireless connection. In particular, an active wireless connection clusters a set of surrounding cells with the target to estimate and reserve future resource requirements, controlling in this way the blocking probability of active calls. 2.3 Dynamic VCT and Shadow Cluster In this section, an improvement of VCT and shadow cluster concepts is proposed. The discussion focuses on VCT, but the reported considerations can be easily extended to shadow cluster. In particular, the analyzed improvement of the VCT is finalized to minimize the VCT handoff problem without resorting, unnecessarily, to resources of the

174 SIMULATION Volume 78, Number 3


WIDEBAND WIRELESS AND WIRED NETWORKS

3. Network Modeling 3.1 Channel Allocation Algorithm

Figure 2. First four levels of the virtual connection tree

wired network. The solution is based on the consideration that if a user transits slowly from one cell to another, or is even still, it is useless assigning him or her a large VCT. In fact, the user will move, at most, in the cells contiguous to the current one. By arranging a narrow VCT, the waste of wired resources diminishes because only a limited number of virtual connections are assigned to the call. Vice versa, if the user moves rapidly, it is opportune to assign him or her a large VCT to avoid the occurrence of VCT handoffs, which can cause service interruption for certain applications. Specifically, in the proposed solution the VCT dimension is determined dynamically comprehending the cell where the user is located at call start and a given number of surrounding rings (see Fig. 2). The number of these rings is determined by the user mobility characteristics. In particular, the VCT handoff probability, P (VCTh), evaluated later, which depends on user mobility, can be exploited for defining the VCT dimensions in such a way that p(VCTh) < ε, where ε is a given design quantity.

The resource allocation algorithm substantially influences network performance. In the considered system, with microcellular architecture, it is suitable to utilize dynamic resources allocation (DRA) [20]. Such schemes are able to adapt themselves easily to the actual traffic characteristics present in the system and allow network designers to modify cell topology without a new frequency planning. As an example, particular DRA schemes have been proposed for Time Division/Code Division Multiple Access/Universal Mobile Telecommunications System (TD-CDMA-UMTS) [21, 22]. In particular, we refer to the maximum packing algorithm [10-17], which allows an upper bound to be found on the performance of a cellular network that uses dynamic channel allocation algorithms. Moreover, this allocation scheme allows a relatively easy quantitative analysis of network performance. The assignment logic is very simple: a new call is blocked if all possible rearrangements of the existing calls, always respecting the constraints imposed by cochannel interference, do not free enough resources for the new request. With this algorithm, a new service request of a user belonging to the category i, which is in cell j , is accepted if the number of busy channels in each cluster the cell j belongs to is less than or equal to C − xi [11, 14], where C is the total number of channels available in the system and xi is the number of channels required by a category i user. Introducing the state matrix S, whose generic element si,j indicates the number of active users (i.e., users with a call in progress) belonging to category i (i = 1, 2, ..., r) present in cell j (j = 1, 2, ..., M), it is possible to formulate analytically the acceptance condition for the ith category, generalizing the expression in [13]; that is, r

2.4 Cellular Network Topology

xk sk,j + sk,t + sk,u ≤ C −xi ∀(t, u) (j, t, u) ∈ Vj ,

k=1

The considered cellular network is represented by M hexagonal cells arranged in an arbitrary structure. In each cell, a base station connected to the wired ATM network is present. It is supposed that there is appreciable interference only between adjacent cells and, thus, a cluster (i.e., a set of neighboring cells, where it is necessary to use different channels to avoid interference [18]) is composed of three cells. There is a finite number of N users circulating in the network. Such users have been classified in r different categories on the basis of the required service and on the basis of mobility characteristics. Each category includes Ni users that, for their specific service, require xi elementary channels. Such a value, xi , can be easily evaluated for constant bit rate traffic, whereas for variable bit rate traffic, the concept of effective bandwidth can be exploited [19]. There is a total number of C available channels in the system.

(1) where Vj indicates the set of clusters the cell j belongs to and (j, t, u) is the generic element of Vj . Note, however, that as discussed in [11], in some cases the state space determined by equation (1) is larger than the state space determined by the maximum packing algorithm, but the difference in terms of performance can be disregarded. 3.2 User Mobility Concerning mobility, we suppose that a category i user can pass from a generic cell j to an adjacent one, k, with a transition probability pi,j k that can be evaluated by experimental measures on real systems. In the plausible hypothesis that there are no constraints on the number of users that Volume 78, Number 3 SIMULATION 175



can sojourn contemporarily in a generic cell, each cell can be modeled by an infinite server queue (i.e., for each user in the cell, there is a virtual server to consider its sojourn time). The sojourn time, ti , for category i users is a random variable with mean 1/µi and an arbitrary probability density function. This formalization allows us to model user mobility with a closed queuing network which, in the stated hypotheses, admits a product form solution [23]. The cell transition rate µi represents the mobility of category i users. Solving the equations of the mobility model (see the appendix), the average number of users for each category i in a generic cell k, E[nik ], is given by xqp E[nqp ] = N M Q i=1 r=1

eqp

µqp =N M Q , eir xir µir i=1 r=1

(2)

where eik is the relative visit rate to each microcell also obtained by the mobility model. It can be noted that the average number of users, E[nik ] (fundamental for the model described below), is directly proportional to Ni . Therefore, changing only the total number of category i users of the network, E[nir ] can be computed by equation (2) without reevaluating all expressions of the mobility model.

Figure 3. Discrete Markov chain

is given by (m) π(m) = π(0) i i · Pi ,

(4)

(m) where π(0) is the m-step i is the initial state vector and Pi transition probability matrix evaluated by a recursive procedure starting with the single-step transition probability pi,uv . The P (VCTh|j ) is the k + 1th element of the vector π(j ) ; that is,

) = π(ji,k+1

k+1

(j ) π(0) i,u · pi,u·k+1 .

(5)

u=0

The evaluation of Psw (j ), derived later in the case of exponential sojourn time, is given by j Psw (j ) = µpi (µpi + µci ) .

(6)

3.3 VCT Handoff Probability As mentioned previously, the occurrence of a VCT handoff can cause serious inconveniences to multimedia real-time traffic. Such a possibility should be reduced to levels acceptable for the considered applications. In this section, the VCT handoff probability is analytically evaluated in order to establish the tree dimension that forms the VCT itself. Moreover, such a result will be exploited in the remainder of the article to evaluate the forced termination probability of a generic call. Let k be the number of cell rings around the cell in which a new call starts, and let pi,uv be the transition probability from ring u to ring v for category i users. It is possible to have a VCT handoff only after a minimum of k + 1 cell transitions. Then, the VCT handoff probability, by the theorem of total probability, is P (VCTh) =

+∞

P (VCTh|j ) · Psw (j ),

(3)

j =k+1

where P (VCTh|j ) is the VCT handoff probability with j cell transitions and Psw (j ) is the probability of j cell transitions. From this equation, it is possible to see that the dimension k of the VCT tree influences the value of P (VCTh). To evaluate P (VCTh|j ), consider the discrete Markov chain representing the system (Fig. 3). By the Markov chain theory [24], the m-step state probability vector π(m) i

The VCT handoff evaluation in equation (3) cannot be done exactly, being an infinite summation, but, as can be realized quite easily, the summation converges, being lower than a convergent geometric series. As experimentally verified in the numerical example, a good approximation of P (VCTh) can be obtained considering just a few terms of the summation. 4. Analysis of the Service Offered by a Cell 4.1 Service Description Starting from the average number of users in each cell, it is possible to describe and analyze the service offered to subscribers. Each generic category i user generates a new call following an exponential distribution with parameter λi , evaluated in terms of the number of service requests per time unit (hour). The request is accepted in the cell in question, if the acceptance condition (1) is satisfied; otherwise, the request is rejected. Moreover, each call has a duration approximated by an exponential distributed random variable (tci ) with mean 1/µci . On the basis of these hypotheses, the traffic in each cell can be described by a multidimensional continuous time Markov chain (essentially a generalization of the Engset queue). A generic state of the chain is based on the number of active users for each category and can be defined by an r-dimensional vector of type s = (s1 , s2 , ..., sr ).




It is easy to check that the steady-state probabilities, obtained by applying the detailed balance to the rdimensional Markov chain, are [25] n n2 n ... r P (s1 , s2 , . . . , sr )T = P0 1 s1 s2 sr (7)

4.3 Handoff Rate At this point it is necessary to evaluate, for each category of users and for each cell, the handoff rate toward the given cell. To this end, it is necessary first to evaluate the average number of active users for each category and cell. Considering a specific cell j , we have

ρs11 ρs22 · · · ρsrr , with P0 as the normalization factor. The values of s1 , s2 , ..., sr are constrained by the following relation: r

si · xi ≤ C and si ≤ ni (8)

i=1

with i = 1, 2, . . . , r. For each category of users, ni indicates the average number of users for the considered cell as evaluated by (2), si is the number of active users, xi is the number of channels occupied by each active user, and λi is the utilization factor. 4.2 Utilization Factor

E[si,j ] =

mi,j

k · Pi,j (k)

mi,j = min(ni,j , C/xi ), (12)

k=1

where E[si,j ] is the average number of active category i users present in the cell. Pi,j (k) represents, for each category, the probability that in the cell there are k category i users. From equation (7), we have Pi,j (k) = P s1,j , . . . , si−1,j , k, si+1,j , . . . sr,j , si,j , . . . si−1,j, si+1,j , . . . sr,j (13) with

su,j xu ≤ C − k · xi .

u,u =i

The evaluation of the utilization factor must take into account the occurrence of handoffs. There is a handoff when an active user (i.e., a user with a call in progress) transits from one cell to another. Because we supposed, as far as the model is concerned, that the number of users in a cell is equal to its average value, we can suppose the effect of handoffs as an increase of the request rate per user. Therefore, the total request rate, λT i , for category i users is λT i = λi + λH i ,

(9)

where λH i is the additional service request rate due to handoff. The total service rate is the sum of the call termination rate, µci , and the handoff attempts rate, µH i . From the mobility model, the average sojourn time for each user in a cell is 1/µpi ; that is, a user leaves one cell with rate µpi . We have µT i = µci + µpi .

(10)

In the evaluation of load factor, we must also take into account the blocking probability, PBi , of a new call due to the constraints imposed by expression (1) [14]. In fact, it is possible that, in the generic cell j , a call request is rejected if (1) is not satisfied, even if the number of actual calls in the cell j is zero. We have the following expression: µci + µpi , (11) ρi,j = λi + λH i,j 1 − PBi,j where ρi,j is the load factor, PBi,j is the blocking probability of a new call, and λH i,j is the handoff rate to cell j .

Because for category i users µpi is the cell output rate and pi,yj is the transition probability from a generic cell y to cell j , the number of attempted handoffs from cell y to cell j results in ΛH i,yj = E[si,y ] · µpi · Pi,yj .

(14)

The handoff rate per user, λH i,j , which refers to the cell j , is obtained by the ratio between the global attempted handoffs toward cell j and ni,j . We obtain λH i,j =

M

ΛH i,yj

ni,j .

(15)

y=1

5. Network Performance Parameters 5.1 Blocking Probability of a New Call One of the most important parameters to quantify the performance of a cellular network is the blocking probability of a new call (i.e., the probability that the request of a user is rejected due to lack of resources). It is opportune to remember that in a cell, the block of a new call occurs when there is at least one cluster the cell belongs to that does not satisfy the acceptance condition expressed by condition (1). Let P (s, j ) = P (s1,j , s2,j , ..., sr,j ), given by (7), be the steady-state probability for each category of users of the Volume 78, Number 3 SIMULATION 177



number of active users present in cell j . The joint steadystate probability of the entire network P (S) can be approximated by the product of marginal probabilities P (sj ). We have P (S) = P (s1 ) · P (s2 ) · . . . · P (sM ).

(16)

Obviously not all states are allowed, but only those that, for each cell, satisfy relation (1). It must be admitted that the independence approximation used in relation (16) is justified mainly by the necessity of making the problem analytically tractable, but the consequences of such an approximation do not invalidate the results; in fact, as will be shown later, there is an excellent agreement between the results obtained by the analytical model and those obtained by simulation. Let PBi,j = prob{a new call of category i in cell j is blocked} and PNBi,j = prob{a new call of category i in cell j is not blocked}. We have PBi,j = 1 − PNBi,j ; hence, determining PNBi,j is equivalent to determining PBi,j . By considering Figure 4(a), where the cells around a generic cell j are indicated by 1j to 6j , PNBi,j can be evaluated by summing over all the states admitted by relation (1): ·· P (si,j )P (si,1j )P (si,2j ) . . . P (si,6j ). PNBi,j = si,1j si,2j

si,6j si,j

(17) To simplify the numerical evaluation of PNbi,j , it can be observed that (17) is expressed in terms of the number of active users for each category, whereas the acceptance of a new services request is based on the global number of busy channels. Let zj be the number of busy channels in cell j . We have, by the total probability theorem, ·· PNBi,j |z1j ,... ,z6j P (z1j ) . . . P (z6j ), PNBi,j = z1j

z2j

z6j

Figure 4. Reference cells for probability evaluation

∩ (zj ≤ C − xi − z2j − z3j ) ∩ (zj ≤ C − xi − z3j − z4j ) ∩ (zj ≤ C − xi − z4j − z5j ) ∩ (zj ≤ C − xi − z5j − z6j ) ∩ (zj ≤ C − xi − z6j − z1j )}. The procedure to evaluate PNBi,j can be further simplified by absorbing the constraint of the maximum packing algorithm in (18) through a suitable choice of the extremes of the summations: PNBi,j =

zj =0

z1j

···

z2j

z6j

(20)

P (zj )P (z1j ) . . . P (z6j ), with zj + z1j + z6j ≤ C − xi . The network new call blocking probability for category i users can be evaluated by a weighted average of PBi,j :

(18) where, as before, we use an independence approximation

C−xi −zj −z5j

C−xi C−xi −zj C−xi −zj −z1j

PBi =

M

ni,j /Ni PBi,j .

(21)

j =1

P (z1j , z2j , z3j , z4j , z5j , z6j ) = P (z1j )P (z2j ) . . . P (z6j ). The various factors P (zj ) can be evaluated by P (si,j )∀si,j P (zj ) = si,j

s1,j x1 + . . . + sr,j xr = zj ≤ C s1,j ≤ min(ni,j ; C/xi )i = 1, . . . , r

(19)

The previous expressions are mutually dependent. In fact, to calculate PBi,j , it is necessary to evaluate ρi,j , which depends on PBi,j . Then, the expressions can be solved by iterated substitutions to obtain a good approximation for PBi,j . Similar approaches have been followed by other authors [14], and the common experimental experiences show that the convergence of PBi is always achieved.

.

The probability can be evaluated by applying the algorithm of maximum packing to cell j : PNBi,j |z1j ,... ,z6j = P {(zj ≤ C − xi − z1j − z2j )

5.2 Handoff-Blocking Probability Also in this case, it is preferable to evaluate the nonblocking probability. The number of global successful handoffs ΛAhi,w for category i users toward the cell w, exploiting (14), is




ΛAH i,w =

M

the cell sojourn time has an exponential p.d.f., we have the following expressions [26]: ΛH i,yw PAH iyw ,

(22)

j Psw (j ) = µpi (µpi + µci ;

where PAH i,yw indicates the successful handoff probability attempted by a category i user from a cell y to a cell w. The ratio between the successful handoffs (given by (22)) and attempted handoffs (given by (14)) provides the successful handoff probability in cell w. Finally, the handoff-blocking probability of a category i user toward a cell w results in M (23) ΛH i,yj . PBH i,w = 1 − ΛAH i,w

PF T i|j = [1 − PBH i ]j −1 PBH i .

y=1

y=1

To evaluate PAH i,yw , we can follow a procedure similar to the one used for evaluating the blocking probability of a new call. Referring to Figure 4(b), in which cells y and w have neighbors 1w , 2w , ..., 5w , the evaluation of PAH i,yw can be evaluated following the same arguments used for the evaluation of PNBi,j . Remembering the quantities zj and P (zj ), we can show that

zw =0

zw1

zw2

C−xi C−xi −zw C−xi −zw −zw1

PAH i,yw =

(24)

C−xi −zw −zw5

···

P (zw )P (zw1 ) . . . P (zy ),

(27)

6. Numerical Results To verify the model validity, establishing eventual limits of application, we compare the analytical results with those obtained by a discrete event simulation of the system. In particular, to implement the simulation program, we exploit the SMPL language [27]. In the graphs, plain lines represent analytical results whereas plus signs (+) represent simulation results. 6.1 Analyzed System To study the system, we refer to a domain subdivided into 10 cells, as shown in Figure 5. It is supposed that the VCTs are of unitary dimension; this implies that for each new call, the system allocates seven virtual connections of wired network. In this example, for the sake of simplicity, we use the same transition probability matrix, shown in Table 1, for all categories of users.

zy

with zy + zw + zw1 ≤ C − xi . The handoff-blocking probability of the entire network for category i users is given by a weighted sum of handoffblocking probability relative to the single cells: PBH i =

M

ΛH i,w · PBH i,w

w=1

M

ΛH i,w .

(25)

w=1

5.3 Forced Termination Probability Forced termination probability (i.e., the probability that an active call is aborted) occurs when there is a blocked handoff during a call or when there is a VCT handoff. Thus, for category i users, by the theorem of total probability, considering that a user can transit from one cell to another several times, we have PF T i = P (VCTh) +

+∞

PF T i|j · Psw (j ),

(26)

j =1

where the value for P (VCTh) is evaluated by (3), PF T i|j is the forced termination probability with j cell transitions, and Psw (j ) is the probability of j cell transitions. When

6.2 Comparison between Analytical and Simulation Results In this specific experiment, we decided to consider three categories of users (i = 1, 2, 3): the communications of users belonging to category 1 require only one radio channel, those of category 2 require two channels, and those of category three require 4 channels. In the network, there are present globally N1 = 30 users of category 1, N2 = 18 users of category 2, and N3 = 12 users of category 3. Moreover, it is supposed that the three categories have the same request rate, λ, and service rate, µc (the average communication time is fixed at 3 minutes). In the first series of figures (Figs. 6-8), system performance versus the request rate, λ, are reported by supposing C = 12 available channels for the entire network and fixing µp = 20 transactions per hour. The analysis of the results shows a substantial agreement between the values obtained by the analytical study and the results obtained by the simulation, confirming in this way that the analytical model provides a good description of the real system. As expected, network performance tends to an asymptotic value, determined by the network capacity, and is different in relation to the three categories of users. The greater the number of required channels, the greater is the blocking probability. Volume 78, Number 3 SIMULATION 179



Table 1. Transition probability matrix Cell

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10

0 0.15 0 0.25 0.15 0 0 0 0 0

0.25 0 0.25 0 0.15 0.15 0 0 0 0

0 0.15 0 0 0 0.15 0.25 0 0 0

0.25 0 0 0 0.15 0 0 0.25 0 0

0.5 0.35 0 0.5 0 0.25 0 0.5 0.35 0

0 0.35 0.5 0 0.25 0 0.5 0 0.35 0.5

0 0 0.25 0 0 0.15 0 0 0 0.25

0 0 0 0.25 0.15 0 0 0 0.15 0

0 0 0 0 0.15 0.15 0 0.25 0 0.25

0 0 0 0 0 0.15 0.25 0 0.15 0

Figure 5. Reference cellular network

Figure 7. Handoff-blocking probability

Figure 6. Blocking probability of a new call

Figure 8. Forced termination probability

6.3 Influence of Mobility We remember that as soon as a user starts a new call, a VCT is reserved for such a call. The communication is interrupted in the case of the user crossing the VCT border. This implies that an increase of mobility corresponds to an increase of VCT handoff probability and hence an increase of forced termination probability. Figures 9 to 11 show values of mobility from 5 to 50 cell transitions per hour. As can be observed, the performance parameters behave differently than a mobility increase: PB and PBH have a small decrease, whereas PF T increases. This behavior

is determined by the interdependence that exists between the duration of a call and the permanence time in a cell. An increase of mobility corresponds to a greater number of handoffs, and hence the increase of forced termination probability is intuitive. On the other hand, because PF T increases, it corresponds to a load reduction: in every cell, the channels will be released earlier, and as a consequence, more new calls and handoffs can be accepted.




Figure 9. Blocking probability of a new call versus mobility

mination, or cell transition. Cell sojourn time, call duration, and interarrival times (distinguished for the three categories) are generated randomly by suitable exponential distributions. A cell transition process follows the transition probability matrix. The simulation program allows us to collect, for each category of users, the number of attempted calls, Tn , blocked new calls, Bl , successful calls, Sc , attempted handoffs, Thf , and blocked handoffs, Bhf . Exploiting such quantities, it is possible to estimate the values of the main system performance indices. The quantities of interest are considered after a suitable warm-up system life, discarding in this way the transient values to approximate their asymptotic values. PB = Bl /Tn

PBH = Bhf /Thf

PF T = (Tn − Bl − Sc )/(Tn − Bl ).

(28)

7. Conclusions

Figure 10. Handoff-blocking probability versus mobility

A study of the integration of broadband wireline and wireless networks was carried out, exploiting the dynamic VCT concept in wired networks, whereas in the cellular domain a dynamic channel allocation scheme was considered. Both number of cells and population of users are finite, which allows real networks to be represented more precisely. The developed model describes accurately, for a wide range of load conditions, the effects produced by user mobility. The performance indices PB , PBH , and PF T were compared with simulation results to assert model validity in the considered situations. Although the specific illustrative example considered in this article is quite simple, the developed model can be applied to fairly realistic networks. In fact, as can be easily inferred, the computational complexity of the model depends on the quite limited number of channels (a few hundred in real systems) and not on the number of users (millions). 8. Appendix

Figure 11. Forced termination probability

The purpose of this appendix is the evaluation of the average number of users per category and cell. The first step is the resolution of the following homogeneous linear system for each category of users: ei,k =

M

ei,j Pi,j k

k = 1, 2, . . . , M

(A1)

j =1

6.4 Simulation Phase An ad hoc event-oriented simulation tool, written using the SMPL language [27], was designed for validating analytical results. In the simulation model, the clock advances when one of these events occurs: new call start, call ter-

to find the relative visit rate ei,k to each cell per each category. The second step, applying the result for queuing networks with infinite servers, allows the distribution of users for each category in the various cells to be found [23]: Volume 78, Number 3 SIMULATION 181



n er,k r,k Nr ! µr,k Nr . M er,q

M r 1 1 ni,k P (n) , ei,k µi,k G k=1 i=1 ni,k !

(A2)

where the departure rate µi,k is equal to µi for each cell, n = (n1 , n2 , ..., nM ) and ni = (ni,1 , ni,2 , ..., ni,r ). The normalization constant G, in this specific case, can be evaluated in closed form using the polynomial formula G= ··· · n1,1 ,... ,n1,M nr,1 ,... ,nr,M M M k=1 n1,k =N1 k=1 nr,k =Nr

=

n1,1 ,... ,n1,M M k=1 n1,k =N1

n n M M

1 e1,k 1,k 1 er,k r,k · ··· n ! µ1,k n ! µr,k k=1 1,k k=1 r,k

n n M M

1 e1,k 1,k 1 er,k r,k ··· n ! µ1,k nr,1 ,... ,nr,M k=1 nr,k ! µr,k k=1 1,k M k=1 nr,k =Nr

N M e1,k 1 =

=

µ1,k

k=1

r

··· ·

N1 !

k=1

µi,k

i=1

nr,k !

Again, applying the polynomial formula, we get  M Ni −ni,j nj,i ei,k µi,k       k=1 r

 ei,j µi,j   k =j Ni      . P (nj ) =    M M ni,j      i=1  e1,k µ1,k ei,k µi,k  

k=1

k=1

  r

eq,j µq,j  Nq    P (ni,j ) =  M nq,j    n1,j ,... ,ni−1,j ,ni+1,j ,... ,nr,j q=1 eq,k µq,k k=1



M

Nq −nq,j

eq,k µq,k    k=1   k =j    × M     eq,k µq,k  k=1

n1 ,... ,nj −1 ,nj +1 ,... ,nM



r 1 1 ni,j = ei,j µi,j G i=1 ni,j !

  ei,j µi,j  Ni    =  M ni,j    ei,k µi,k

M

k=1

k =j

1 n1,k !

e1,k µ1,k

n1,k

1 ··· nr,k !

n r

1 ei,j i,j = ni,j ! µi,j i=1

n1,k !

er,k µr,k

nr,k

M

n1,1 ,... ,n1,j −1 , k=1 n1,j +1 ,...n1,M k =j

n1,k

e1,k N1 ! µ1,k N × . . . M e1,q 1 q=1

ni,j

n1 ,... ,nj −1 ,nj +1 ,... ,nM k=1

nq,i

where Ni is the total number of users belonging to the ith category and the arrival rate ei,k is evaluated by (A1). The marginal state probability with respect to cell j is P (nj ) = P (n1 , n2 , . . . , nM )

×

µr,q

q=1



,

Ni !

nr,1 ,... ,nr,j −1 , k=1 nr,j +1 ,...nr,M k =j

µr,k Nr !

Ni M ei,k

M

The marginal state probability with respect to cell j and category i is

Nr M er,k k=1

... ×

µ1,q



M

nq,j

  Nq r

eq,j µq,j  Nq    ×  M nq,j    q=1 nj,q =0 q =i eq,k µq,k k=1



Nq −nq,j

M eq,k µq,k    k=1   k =j    × M     eq,k µq,k  k=1



Ni −ni,j

ei,k µi,k    k=1   k =j      M    ei,k µi,k  k=1






ni,j

  N  ei,j µi,j   = i   M ni,j    ei,k µi,k



M

Ni −ni,j

ei,k µi,k    k=1   k =j      M    ei,k µi,k 

k=1

,

k=1

recalling the Newton binomial M Nq −nq,j nq,j eq,k µq,k       k=1 Nq     µ e Nq  q,j q,j   k =j  = 1.    M M nq,j      nq,j =0  eq,k µq,k eq,k µq,k  

k=1

k=1

Therefore, the marginal state probability with respect to cell j and category i is a binomial random variable. Thus, the average number of users at category i in microcell j , E[ni,j ], results in xqp E[nqp ] = N M Q i=1 r=1

eqp

µqp =N M Q . eir xir µir i=1 r=1

9. References [1] Acampora, A., and M. Naghshineh. 1994. An architecture and methodology for mobile-executed handoff in cellular ATM networks. IEEE Journal on Selected Areas in Communications 12:1365-74. [2] Acampora, A. 1996. Wireless ATM: A perspective on issue and prospects. IEEE Personal Communications, August, 8-17. [3] Veeraraghavan, M., M. J. Karol, and K. Y. Eng. 1997. Mobility and connection management in a wireless ATM LAN. IEEE Journal on Selected Areas in Communications 15 (1): 50-68. [4] Jiang, S., D.H.K. Tsang, and S. Gupta. 1997. On architectures for broadband wireless systems. IEEE Communications Magazine, October, 132-40. [5] Reininger, D., R. Izmailov, B. Rajagopalan, M. Ott, and D. Raychaudhuri. 1999. Soft QoS control in the WATMnet broadband wireless system. IEEE Personal Communications, February, 34-43. [6] Keller, R., B. Walke, G. Fettweiss, G. Bostelmann, K. H. Mohrmann, C. Herrmann, and R. Kraemer. 1999. Wireless ATM for broadband multimedia wireless access: The ATMmobil project. IEEE Personal Communications, October, 66-80. [7] Lee, J., T. Jung, S. Yoon, S. Youm, and C. Kang. 2000. An adaptive resource allocation mechanism including fast and reliable handoff in IP-based 3G wireless networks. IEEE Personal Communications, December, 42-7. [8] Muratore, F., ed. 2000. UMTS mobile communications for the future. New York: Wiley. [9] Levine, D. A., I. F. Akyildiz, and M. Naghshineh. 1997. A resource estimation and call admission algorithm for wireless multimedia networks using the shadow cluster concept. IEEE/ACM Transactions on Networking 5 (1): 1-12.

[10] Everitt, D., and D. Manfield. 1989. Performance analysis of cellular mobile communication systems with dynamic channel assignments. IEEE Journal on Selected Areas in Communications 7:1172-80. [11] Raymond, R. 1991. Performance analysis of cellular networks. IEEE Transactions on Communications 39:1787-93. [12] Everitt, D. E., and N. W. Macfadyen. 1983. Analysis of multicellular mobile radiotelephone systems with loss. BT Technology Journal 1 (2): 37-45. [13] Kelly, F. P. 1986. Blocking probabilities in large circuit-switched networks. Advances in Applied Probability 18:473-505. [14] Pallant, D. L., and P. G. Taylor. 1994. Approximation of performance measures in cellular mobile networks with dynamic channel allocation. Telecommunication Systems 3:129-63. [15] Kulshreshtha, A., and K. N. Sivarajan. 1999. Maximum packing channel assignment in cellular networks. IEEE Transactions on Vehicular Technology 48:858-72. [16] Borst, S., and P. Whiting. 2000. Achievable performance of dynamic channel assignment schemes under varying Reuse constraints. IEEE Transactions on Vehicular Technology 49:124864. [17] Pallant, D. L., and P. G. Taylor. 1995. Modeling handover in cellular mobile networks with dynamic channel allocation. Operations Research 43 (1): 33-42. [18] Mac Donald, V. H. 1979. The cellular concept. Bell System Technical Journal 58 (1): 15-41. [19] Kesidis, G., J. Walrand, and C. S. Chang. 1993. Effective bandwidths for multiclass Markov fluids and other ATM sources. IEEE/ACM Transactions on Networking 1:424-8. [20] Katzela, I., and M. Naghshineh. 1996. Channel assignment schemes for cellular mobile telecommunication systems: A comprehensive survey. IEEE Personal Communications, June, 10-31. [21] Dahlman, E., B. Gudmundson, M. Nilsson, and J. Skold. 1998. UMTS/IMT2000 based on wideband CDMA. IEEE Communications Magazine, September, 70-80. [22] Mihailescu, C., X. Lagrange, and P. Godlewski. 1999. Dynamic resource allocation for UMTS TD-CDMA systems. Paper presented at EPMCC’99, Paris, France, March. [23] Baskett, F., K. M. Chandy, R. R. Muntz, and F. G. Palacios. 1975. Open, closed and mixed networks of queues with different classes of customers. Journal of the ACM 22:248-60. [24] Gross, D., and C. M. Harris. 1985. Fundamentals of queueing theory. New York: Wiley. [25] Bertsekas, D., and R. Gallager. 1992. Data networks. Englewood Cliffs, NJ: Prentice Hall. [26] Rappaport, S. S., and L. Hu. 1994. Microcellular communication systems with hierarchical macrocell overlays: Traffic performance model and analysis. Proceedings of the IEEE 82:138397. [27] MacDougall, M. H. 1987. Simulating computer systems: Techniques and tools. Cambridge, MA: MIT Press.

Paolo Arseni received a doctorate engineering degree in electrical engineering from the Politecnico di Bari, Italy, in 1998. His research interests span the fields of wireless networking and design and analysis of IP networks. From 1998 to 1999, he worked for a telecommunication company (Alcatel S.p.A.) as a radio network planner. Since December 1999, he has been working at Banca121 on Internet and mobile banking applications. Gennaro Boggia received, with honors, a doctorate engineering degree in electrical engineering 1997 and a PhD in electronic

Volume 78, Number 3 SIMULATION 183



engineering in 2001, both from the Politecnico di Bari, Italy. From May 1999 to December 1999, during his PhD program, he was a visiting researcher at the Centro Studi e Laboratori Telecomunicazioni), where he was involved in the study of the core network for the next releases of Universal Mobile Telecommunications Systems (UMTS). His research interests span the fields of wireless networking, cellular communication, queuing networking, and network performance evaluation.

Pietro Camarda received a university degree in computer science from the University of Bari, Italy, in 1978. Since 1986, he has been with the Dipartimento di Elettrotecnica ed Elettronica at the Politecnico di Bari, Italy, where he is currently an associate professor of telecommunication. He was visiting scholar from October 1986 to December 1987 in the Computer Science Department at the University of California, Los Angeles. He has been involved in various research areas, mainly, LAN/MAN architectures and protocols, optical networks, network reliability, cellular radio networks, and telecommunication services.



Modeling Telecommunication Infrastructures Integrating Wideband

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