Advanced Wireless Networks - 4G Technologies

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12.4.4 Performance evaluation

The performance measures of interests, which characterize the GoS, are the probabilities of new-call blocking and handoff failure. In optimization framework, a linear combination of these probabilities is usually used to define the GoS as a cost-function. The weighting factors are usually decided based on the ‘importance’ of calls considering new-call or handoff, user classes, cost of service classes, etc. For example, GoS for a single-class system in Zander Kim [50] has been defined as: GoS ≡ (10F + B), where F is the handoff failure probability and B is the new-call blocking probability. The other important performance measure is the equilibrium QoS loss probability, i.e. the probability of losing communication quality in the system outage state. The Erlang capacity of the system can be determined for given percentages of these loss probabilities. In complete-sharing systems, for all k K and in steady-state condition, denote: Bk as the new-call blocking probability of class-k calls; and Fk as the handoff failure probability of class-k calls. In systems with QoS differentiation, for all j J and k K and in steady-state condition, denote: B jk as the new-call blocking probability of traffic class-( j, k); and Fjk as the handoff failure probability of traffic class-( j, k).

In addition, operators may be interested in group behavior. Thus, for all j J and in steady-state condition, denote: B j as the new-call blocking probability of class- j users; and Fj as the handoff failure probability of class- j users. Finally, denote: Ploss as the equilibrium QoS loss probability.

12.4.5 Related results

In this subsection, the results of extensive studies on product-form loss networks, stochastic knapsack problems and effective-bandwidth allocation [63–68], are summarized, which supports analytical methods used in this section. The single-link with no buffering and complete-sharing loss system is considered. Let the system capacity be C and the offered traffic intensity of class-k is αk = λk /μk , where λk is the Poisson arrival rate and 1/μk is the mean service time of class-k call. Define the set of all possible system states:

The cost of computation with the above formula can be prohibitively high for larger-size state set, i.e. for large K and C/wk . This problem has been considered by many authors, resulting

in elegant and efficient recursion techniques for the calculation of blocking probabilities. For practical evaluation purposes of this section, i.e. keeping it accurate, but as simple as possible without loss of generality, the stochastic-knapsack approximation described in References [63, 66] is chosen and believed to suite best investigating various load-based and cost-effective CAC policies.

Define the set of all feasible system load states:

The steady-state probability of the load state c is given by:

c

where q(c) is given in a recursive form as follows:

The blocking probability of class-k calls now can be determined by:

c :c>C−wk

12.4.6 Modeling-based static complete-sharing MdCAC system

The above results can be applied directly for analyzing this system with the parameters as follows: the system capacity is Ca instead of C; αk = (λl,k + λhl,k )/(μ1 + μ2). Then, Bk is obtained by using Equation (12.24):

Given the offered traffic intensity of each service class, the performance of the system strictly depends on Ca and w, which are needed a priori. Overestimates or underestimates of these parameters may result in wasting or insufficiently allocating resources, thereby reducing the GoS or lowering the perceived QoS, respectively. Furthermore, in the presence of additional uncertainty causing the changes in traffic descriptor parameters, the system cannot provide appropriate QoS to the users and therefore Ca and w need to be redesigned.

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However, with a reliable modeling, good overall statistical multiplexing gain and performance can be expected. From the TDMA/GSM experiences, static channel allocations in some circumstances can even provide better capacity gain than dynamic ones. Note that Ca and w can be improved, i.e. maximizing Ca while keeping w as low as possible for given QoS requirements, by using techniques like sectorization, multiuser detection, smart antennas, etc.

12.4.7 Measurement-based complete-sharing MsCAC system

MsCAC should overcome the nonrobustness problem of MdCAC described above. The network side attempts to learn statistics of the traffic by online measurements. Under the assumption (2) of the traffic model, stationary wk and Ca are bounded Gaussian random variables having mean wk and Ca, and variance σk2 and 2 respectively. Here, Ca and wk denote the random variables and also their mean values. The variances can be estimated by using corresponding boundary and mean values. Let β be the acceptable equilibrium outage probability of the system.

The goal is to quantify and to illustrate the system behavior with its sensitivity to estimation errors, and to lay the groundwork for studying the scaled aggregate UL load fluctuations of the traffic with more sophisticated models. It does not aim to study details of any specific measurement-based CAC algorithms, neither to provide the parameter estimation framework. Some valuable results for measurement-based CAC in single-class systems can be found in Dziong et al. [57], whereas Sampath and Holtzman [58] investigate measurementbased CAC algorithms by simulations. Herein, the multivariate Gaussian approximation is used to dimension the admissible region. In the MsCAC system, stationary constraints of the system capacity can be defined by:

1/2

The components of Equation (12.29) are obtained by online estimations. The additive uncertainty due to measurement errors may have significant impacts on the system performance. In addition, the need for reliable estimations of mean and variance values for various service classes and cell-basis may result in far more complex hardware/software implementations compared with the modeling-based policies. The performance characteristics of the MsCAC system will be obtained by simulations of a simple memoryless and an auto-regressive measurement-based system. The over-bounding hyperplane of the admissible region can be determined by intersection of the axes in M-dimensional Euclidean space. The intersection point (0, 0, . . . , ck , 0, . . . , 0) corresponds to the single-class capacity region of class-k that is given in estimation by:

For the Gaussian estimation errors, ck can be quantified by:

where ε, δ are N (0, 1) normal random variables [57] representing impacts of measurement errors. It has been shown in Sampath and Holtzman [58] by simulations that measurementbased CAC policies are best suited for serving quite bursty traffic. Their performance is almost the same, and none of them are capable of meeting the loss targets accurately. One can reach the same conclusion from the above analysis.

12.4.8 Complete-sharing dynamic SCAC system

It has been shown [64, 66, 67] that for larger C/wk systems, which is true in WCDMA cellular systems, the stationary behavior of system load states c approaches the one-dimensional Markov process. Thus, for analysis of the SCAC system we invoke Equations (12.21)– (12.23) with the following modifications. The system capacity is now Cu. The behavior of the system when the system load state is less than Cl is exactly the same as that of the complete-sharing system. When the system load state is between Cl and Cu, a soft decision is used for the acceptance of a new call. The highest priority is given to a handoff call. Equation (12.23) now becomes:

π k (c) is the admission probability of a new call given by Equation (12.11) or (12.12);(c) is the function of system load state representing the call-drop rate due to loss of the communication quality. For instance, a linear model for (c) with a constant empirical weight-factor ξ can be defined as follows:

The performance measures are obtained as follows:

c

With this SCAC, GoS including new-call blocking probability and handoff failure probability can be significantly improved over MdCAC and MsCAC. However, in complete-sharing systems, beyond a certain load state, higher resource-consuming users hardly can gain access into the system if the traffic intensity of lower resource-consuming users is relatively heavy. This can be overcome by using QoS differentiation combined with SCAC for meeting potential customer demands.

design of such dynamic control mechanisms, there is a need for precise understanding of the dynamics of available UL radio resources for NRT packet transmissions while RT traffic is being served adequately. The main purpose of this section is to provide a reliable method based on asymptotic and quasi-stationary analysis of the RT traffic, to predict free capacity and average upper limits of UL data throughput. Based on the prediction results, a simple and effective DFIMA scheme is proposed for NRT packet access control.

12.4.12 Assumptions

Denote Rp as the bit-rate for packet-data transmission in UL, Lp as the packet-length in bits, γp as the SIR target to meet the QoS requirements of packet transmission and Tp as the transmit time interval (TTI) needed for a packet at the air interface, Tp = Lp/Rp. The following assumptions are made in addition to those made earlier in this section.

(1)RT services have higher priority over NRT messaging services. Resource consumption of the NRT packet-service domain should never exceed the free resources left by the RT traffic.

(2)Users are sharing common channel for NRT packet access in UL using different DS/CDMA code sequences. The amount of UL resources consumed by a packet transmission can be determined similarly to the resource consumption of an RT connection that is given in Equation (12.1). The parameters needed for packet transmissions can be predefined or decided by the access control.

(3)The time axis is divided into Ts-long time-slots for packet transmissions, which can be equal to one or multiple radio-frame duration of, e.g., 10 ms as defined in 3GPP standards. Packet transmissions are synchronized starting at the beginning of a time-slot.

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(4a) Without QoS differentiation, Tp is set equal to Ts. Thus, packet transmissions are synchronized starting at the beginning and finishing at the end of the same time-slot. For a given time-slot, all transmissions have the same bit-rate and SIR target that may be changed on slot-by-slot basis.

(4b) For different user classes, QoS differentiation should guarantee different maximum delays and minimum data rates when sending messages, e.g. emails, pictures, etc. Therefore, packet transmissions may have different parameters (bit-rate, SIR target, TTI) and resource consumption, which are controlled by the access control taking into account QoS differentiation paradigms.

12.4.13 Estimation of average upper-limit (UL) data throughput

Let free capacity of the system left by the RT traffic at time t be z(t). The stationary distribution and quasi-stationary behavior of z(t) over a sustained period of time are of interest. Let c(t) be the RT system load state at time t and C(t) is the system ‘soft’ capacity at time t. Hence:

where z and c are the free capacity and the RT system load state in equilibrium condition. The z and c process itself is not Markovian in general, but for larger Ca/wk it behaves as an approximate Markov process. The quasi-stationarity of c over time interval τ is approximated by an exponential function [64, 69].

For instance, to obtain the equivalent one-dimensional birth–death process for z and c in complete-sharing systems, the Pascal approximation can be used as in Grossglauser [67]. First, we need to scale the system capacity and resource consumption of each RT service class into integers. To do so we first assume min{wk , k K}≡ w1. Then define the scaled load vector, the scaled system state and the scaled average system capacity as follows:

w* = {w*k , k K} ≡ { wk /w1 , k K}; c* ≡ c/w1 ; and

C*a ≡ Ca /w1 respectively.

The set of equivalent system states is then given by:

ψ * ≡ c* : c* = 0, 1, 2, . . . , Ca*

Normalize the mean service-time of a RT call: μ ≡ 1. The equivalent birth–death process being in steady state c* has a death rate of c* and a birth rate of:

The quasi-stationary probability of RT traffic being in load state c* over period of time τ can be defined by:

Using the exponential property of quasi-stationary probability in loss networks mentioned above, Equation (12.64) can be approached by:

Equation (12.65) for τ = Tp provides the equilibrium probability that there are maximum z* = C*a − c* units of resources available for packet transmissions. Let S(c*) be the upper-limit number of packets that can be transmitted successfully in a given time-slot, for a given load state of the RT service domain c*.S(c*) can be calculated by:

(C* − c*)w

S(c*) = p(c*, Tp) a 1 (12.66)

Rpγp/ W

The above equation can be used to study tradeoffs of the parameters for optimal packet access. Let us assume that there are N data users, each generating data-packets according to the Poisson process with rate per time-slot, ≤ 1. Hence, there are D = N average active data-sources per slot. If each of them attempts to transmit their packets at the beginning of a given time-slot with the probability of min[1, S(c*)/D], the probability of successful packet transmission, i.e. having less than S(c*) initiated transmissions, is at least 1/2. This is in accordance with the binomial distribution. The average upper-limit of UL packet-data throughput denoted by S is given by:

c* *

where Ploss is the QoS loss probability. By using Little’s formula, the average lower limit of packet delay is given by S/D time-slots.

12.4.14 DFIMA, dynamic feedback information-based access control

The NRT packet access in UL needs to adapt to a quasi-stationary stochastic process of free capacity left by the RT traffic. DFIMA scheme is a promising candidate to optimize UL packet transmission characteristics and RRU. The motivation behind this scheme is as follows. Data terminals attempt to transmit their packets with a transmit permission probability (TPP), bit-rate and TTI changing dynamically on slot-by-slot basis according to the feedback information from the network. Similar access control schemes have appeared in different contexts. For instance, Rappaport [71] investigated the feedback channel state information-based carrier sensing MAC protocols for a centralized asynchronous CDMA packet radio system. Thomas et al. [70] proposed a real-time access control scheme for