ADMISSION AND FLOW CONTROL FOR MULTIMEDIA CDMA Cristina Comaniciu, Narayan Mandayam
David Famolari, Prathima Agrawal
WINLAB, Rutgers University ccris,
[email protected]
Telcordia Technologies fam,
[email protected]
ABSTRACT QoS guarantees for an integrated CDMA system can be provided by a combination of admission and flow control. The admission control restricts the number of users in the system such that QoS requirements for all calls can be met. The flow control balances the system interference on a slot by slot basis such that Bit Error Rate requirements are met for all users and the real time users are given the highest priority. In this paper, we analyze the scenario of a single cell DS-CDMA system carrying both voice and www users. A new admission control is proposed and analyzed for web browsing sessions. The challenge in designing admission control for web users is due to the fact that the web traffic description is based on heavy tailed distributions. Thus, an accurate estimate for the average offered rate for a web session is hard to compute. Our proposed admission scheme, adaptively modifies the threshold at each time slot based on new average load measurements. The admission threshold is computed such that the probability of session dropping is maintained below a prescribed value. The flow control mechanism is an extension of the one proposed in [9], where the residual capacity from voice users is used to allocate resources for www users. 1. INTRODUCTION There is a great amount of interest nowadays in designing frameworks to provide QoS guarantees for wireless multimedia services [2], [3], [4]. However, few papers consider non Poisson traffic in wireless systems. There is a large amount of work in ATM networks that models Ethernet and WAN traffic as self-similar processes [5] [6]. The self-similar traffic is obtained as a result of multiplexing many on/off sources with heavy-tailed On and/or Off period lengths [6]. The aggregate traffic is modeled as Fractional Brownian Motion (FBM). This model is valid if the traffic is aggregated from a large number of sources and also if the effect of flow control on any user is negligible [8]. In a CDMA cell, the number of web users may not be large enough for the assumption of self-similarity to hold. Moreover, there is flow control that affects each user’s traffic. Thus, it is more appropriate to design an access mechanism by considering models for web browsing sessions, rather than an FBM model for the aggregate traffic. In [11], models for web browsing sessions for downlink, and large file uploads and reverse traffic for web sessions for uplink are recommended for testing in the cdma2000 system. There has also been recent work on web browsing models for users in a wireless radio network [7]. In this paper we propose a two level access control for an integrated CDMA system carrying voice and www users. The QoS for both kinds of traffic is guaranteed by a combination of admission This work is supported in part by the NSF under Grant No. NCR 9706036 and by Telcordia Technologies
and flow control. The admission control allows a particular user to be connected, if, after admission, QoS specifications for all users can be met. The admission control acts at a call arrival time scale. The flow control gives priority to the voice users. It balances the system interference on a slot by slot basis by scheduling more data users to transmit when the number of active voice users is is low, and less data users when the voice load is high. In this paper we focus on designing an admission control scheme for the web users. The challenge is that the web browsing model is characterized by a heavy tailed distribution and the average offered rate per www user is hard to estimate. Thus, an adaptive admission control algorithm based on average load estimation using measurements is proposed. A new www user is admitted if the average measured load is less than a threshold, computed such that the QoS requirements (data delay) can be met with high probability. Our work is motivated by [10] which discusses admission control for ATM networks. [10] proves that significant statistical multiplexing gains can be achieved if the admission criterion is based on instantaneous load measurements and the admission threshold is derived using a decision theoretic approach. For the flow control mechanism, we use an extension of the algorithm proposed in [9], which exploits the residual capacity from voice users, to allocate resources for www users. 2. SYSTEM MODEL AND FRAMEWORK We consider access control for an integrated voice/www users, single cell CDMA system. The analysis is for the uplink, which is considered to be slotted. We analyze the simplest case of perfect power control. As in [9], the voice source is characterized by an ON/OFF 2 state Markov model, with an activity coefficient α = 0.4. The web browsing traffic is described as in [11]: • Poisson arrivals of sessions (arrival rate λS ); • Geometrically distributed number of packet calls per session; • Geometrically distributed inter-arrival time between packet calls; • Pareto distributed number of packets per packet call (Np ); • Geometrically distributed inter-arrival time between packet arrivals (Ti ); • Fixed packet size. All numerical results were obtained using the system and data model parameters specified in Table 1. As in [9], the Bit Error Rate (BER) requirements are mapped to target SIRs (Signal to Interference Ratios). Thus, the BER requirements for all calls can be met if the following condition holds [1]:
Table 1: Numerical values for analysis and simulation results System bandwidth target SIR voice target SIR www number of voice users in the system mean packet interarrival time discrete unit of time for packet interarrival probability of a new packet arrival probability of a new packet call initiation in the next time slot mean number of packet calls per session mean interarrival time between packet call initiations new session arrival rate per second Pareto distribution parameter Pareto distribution parameter length of a packet (measured in units of length of voice packets) time slot performance tolerance dropping probability constraint
W SIRv SIRwww
1.25 MHz 7 dB 10 dB
Nv t
30 0.01 seconds
ti
0.001 seconds
pi
0.2
pc
0.0001667
The admission control algorithm will be discussed in detail in the next section. The flow control schedules the system resources such that condition (2) holds for each time slot. Therefore, the flow control condition for the nth slot is given by: nwww
SIRv ∗ Rv ∗ nv (n) + SIRwww
(Rwww (n))j ≤ W (1 − η).
j=0
(4) The flow control algorithm proposed in [9] predicts the residual capacity available for data in the next time slot based on current measurements on the number of active voice users nv . After prediction, the total rate allocated for data for the next slot is given by:
Rtot (n + 1) = µNpc
X
5
W (1 − η) − SIRv ∗ Rv ∗ c nv (n + 1) , SIRwww
(5)
and can be distributed among requesting users in a round-robin fashion.
µTpc
120 seconds
λs
1 session/second
3. ADMISSION CONTROL FOR WWW USERS
a
1.1
Using the admission condition (3), the aggregate average rate reservation for the www users is given by:
b
2.7 ∗
n Ts ǫ
20 0.02 seconds 0.1
ψ
0.025
R =E
"n www X
(Rwww )j
j=0
#
=
W (1 − η) − SIRv ∗ Rv ∗ E[nv ] . SIRwww
(6) We map the delay requirement for a www user into a data offered load condition for the system. The offered load for the web sessions is defined as: www Rav , (7) R∗ www where Rav is the average total offered rate per aggregate web traffic. The role of the admission control is to keep ρwww close to some target value ρt . Hence, the admission control condition is:
ρwww =
Z=
nX nv www SIRwww 1 X (SIRv )i + ≤ (1 − η) , (1) Gv Gwww j i=0
j=0
where Z represents the system load and nv and nwww represent the number of active voice and www users, respectively. SIRv and SIRwww are the target SIRs for voice and www users, respectively, Gv and Gwww are the spreading gains for voice and www users. η represents the ratio of the the background noise level to the total received interference [1]. Considering same SIR requirements for a particular class of traffic (voice or web sessions), and denoting Rwww as the transmission rate for a www user, condition (1) can be rewritten as:
www Rav ≈ ρt . R∗
(8)
Thus, the adaptive admission control we propose, can be summarized as: At the end of each time slot n: • measure the new total offered load averaged over the last Wsize slots:
nwww
Z = SIRv ∗ Rv ∗ nv + SIRwww
X
(Rwww )j ≤ W (1 − η),
j=0
(2) where Rv is the basic transmission rate for a voice user (9.6Kb/s). Both admission and flow control rely on condition (2). The admission control ensures that (2) holds in an average sense. Thus, the admission condition is: # "
n
ρm (n) =
X 1 (Narrivals )j , min{n, Wsize }
(9)
j=δ
where δ = max{0, n − Wsize }, (Narrivals )j = the number of packets arriving in slot j. • Admit all new connection requests in the next time slot, if
nwww
SIRv ∗Rv ∗E[nv ]+SIRwww E
X
(Rwww )j
≤ W (1−η),
∆ρ(n) = (ρt − ρm (n)) ≥ Tρ
(10)
j=0
(3)
Otherwise, reject all new connections for the next time slot.
Tρ is the admission threshold which is set such that, with certain probability, the load for the next slot (after admission) will be less than ρt + ǫ, where ǫ is the acceptable performance loss tolerance. The average rate offered per packet call is a random variable specified as: Rpc =
Pdrop (∆ρ, Ni ) =
Ni ∞ ∞ X XX
Pdrop (∆ρ, Ni )|i, j, k) ∗
(21)
i=0 j=1 k=0
∗PNs (k) ∗ PTi (j ∗ ti ) ∗ Pni (i).
Np ∗ n . (Np − 1) ∗ Ti
(11)
t The total new rate offered in the next time slot (Rnew ) is caused by new session arrivals, and by new packet call initiations from previously admitted sessions, currently inactive. The number of new sessions (Ns ) is Poisson distributed with rate λs ∗ Ts sessions per unit slot Ts , and the number of new packet call initiations in the next time slot is a Binomial distributed random variable (ni ). Therefore, the total new offered rate is a random variable expressed as: t Rnew = (ni + Ns ) ∗ Rpc .
(12)
To simplify the computation, we will make a conservative assumption that no active packet call will end in the next time slot. Hence, the new offered load will be given as: (ni + Ns ) Np ∗ n . (13) ∗ R∗ (Np − 1) ∗ Ti The QoS performance requirements are translated into the following condition: ρnew =
ρm (n) + ρnew (n + 1) ≤ ρt + ǫ,
(14)
The dropping probability dependence on ∆ρ can be neglected. This is due to a very small interarrival time between packets, such that variations in the value of D∗ (∆ρ) have a negligible impact on the value of the dropping probability. In Figure 1, the dropping probability is plotted as a function of both the number of inactive sessions currently admitted in the cell (Ni ) and the arrival rate of new sessions (λs ). For a fixed constraint for the dropping probability (Pdrop ≤ 0.025), the admission threshold is plotted in Figure 2. It can be seen that Tρ is either 0 (for the feasible region) or 1 (infeasible regions). Hence for the first case, all calls can be admitted regardless of how close the current measurement is to the target, provided that ∆ρ ≥ 0, whereas for the second case no call can be admitted for the given pair (λs , Ni ). It can also be noticed that the dropping probability is predominantly affected by the arrival rate of new sessions. Thus, we need an auxiliary admission mechanism to limit the arrival rate of new sessions to a desired target λt = max{λ : Pdrop (λ) ≤ ψ}. The description of the proposed mechanism follows. The base station continuously estimates λbs and broadcasts an admission probability: padm =
or equivalently: ρnew (n + 1) ≤ ∆ρ(n) + ǫ,
(15)
If (15) does not hold, some sessions may be dropped, thus the dropping probability can be defined as: Pdrop = P {ρnew (n + 1) > ∆ρ(n) + ǫ}.
(16)
The admission threshold Tρ is determined as: Tρ = min{∆ρ : Pdrop (∆ρ) ≤ ψ}.
λt
λbs
.
(22)
Each arriving new session will generate a Bernoulli random variable with this probability. If a “1” is generated, the session sends a new call request to the base station; otherwise it refrains to request a new connection and it is blocked. It is assumed that blocked arrivals are not allowed to retry to reconnect. Hence, the number of new connection requests will be a Poisson random variable with arrival rate λt .
(17)
Knowing that Np is Pareto distributed with the characteristic function given by FNp (x) = 1 − (16) becomes:
a b x
, x ≥ b,
(18) 0.2
=
1, 0,
1 − ba ∗ 1 −
n∗(ni +Ns ) D ∗ (∆ρ)∗Ti
Pdrop
Pdrop (∆ρ, Ni )|ni , Ti , Ns ) =
a
if ,
1
n∗(ni +Ns ) if D ∗ (∆ρ)∗T i i +Ns ) − n∗(n D ∗ (∆ρ)∗Ti
0.1 10
≥1 ≥
1 b
otherwise (19) where Ni is the number of inactive web sessions in the CDMA cell, and D∗ (∆ρ) = (∆ρ + ǫ) ∗ R∗ . (20) Thus, the dropping probability can be derived from (19) by averaging over the probability mass functions of the number of new session arrivals, the interarrival time between packets and the number of new packet call initiations from inactive sessions:
8
0 40
6 30
4
20 Ni
2
10
λ
s
0 0
Figure 1: Dependence of dropping probability on the rate of new session arrivals (λs ) (sessions/second), and on the number of inactive sessions in the cell (Ni ).
1
T
ρ
0.5 8
0 6 30
4
20 N
i
10
λ
s
2
Figure 2: Dependence of the admission threshold on the rate of new session arrivals (λs ) (sessions/second), and on the number of inactive sessions in the cell (Ni ).
In Figure 3, a sample path obtained from a simulation implemented using OPNET [12] is presented for a simulation time of 40 minutes. From top to bottom, the figure presents the evolution in time of the number of www sessions admitted in the system, the average measured offered load and the number of www packets arriving in a slot. The average offered load obtained for a simulation period of 40 minutes is ρav = 0.123, which is close to the target ρt = 0.1 for this example. 4. CONCLUSION In this paper a new admission control for web users in an integrated voice/www CDMA system is proposed. Using a similar approach as in [9], the total rate reservation for data can be determined as a function of the number of voice users in the system and the target SIRs for both voice and www traffic. By an analogy with a queueing system, the delay requirements for data can be mapped into a data offered load requirement. Therefore, for a fixed reservation rate, the average aggregate offered rate should be maintained at a prescribed value. The difficulty in realizing this lies on the fact that the average load for a particular web session is hard to estimate since the traffic is described by a heavy tailed distribution. To overcome this problem, we propose a scheme that adaptively modifies the admission threshold at each time slot based on new average load measurements. The admission threshold is computed such that the probability of session dropping is maintained below a prescribed value. Simulation results show that the admission control succeeds in maintaining the measured offered load close to the imposed target load. 5. REFERENCES [1] A.M. Viterbi, A.J. Viterbi. Erlang Capacity of a Power Controlled Cellular CDMA System, IEEE Journal on Selected Areas in Communications, vol 11, No 6, August, 1993, pp. 892900. [2] A. Sampath, J.M. Holtzman. Access Control of Data in Integrated Voice/Data CDMA Systems: Benefits and Tradeoffs, IEEE Journal on Selected Areas in Communications, vol 15, No 8, October 1997, pp. 1511-1526.
Figure 3: Sample path simulation [3] T. Liu, J. A. Silvester. Joint Admission/Congestion Control for Wireless CDMA Systems Supporting Integrated Services, IEEE Journal on Selected Areas in Communications, vol 16, No 6, August 1998, pp. 845-857. [4] S. Choi, K.G. Shin. An Uplink CDMA System Architecture with Diverse QoS Guarantees for Heterogeneous Traffic, IEEE/ACM Transaction on Networking, vol 7, No 5, October 1999, pp. 616-628. [5] W.E. Leland, M.S. Taqqu, W. Willinger, D.V. Wilson. On the self-similar nature of Ethernet traffic (extended version), IEEE/ACM Transaction on Networking, vol 2, No 1, 1994, pp. 1-15. [6] M.E. Crovela and A. Bestavros. Self-Similarity in World Wide Web Traffic: Evidence and Possible Causes, IEEE/ACM Transaction on Networking, vol 5, No 6, December 1997, pp. 835-846. [7] E. Anderlind, J. Zander. A Traffic Model for Non-Real-Time Data Users in A Wirelss Radio Network, IEEE Communications Letters, vol 1, No 2, March 1997, pp. 37-39. [8] A. Erramilli, O. Narayan, W. Wilinger. Experimental Queueing Analysis with Long-Range Dependent Packet Traffic, IEEE/ACM Transaction on Networking, vol 4, No 2, April 1996, pp. 209-223. [9] C. Comaniciu, N.B. Mandayam. Delta Modulation based Prediction for Access Control in Integrated Voice/Data CDMA Systems, IEEE Journal on Selected Areas in Communication (JSAC), vol 18, No 1, January 2000, pp. 112-122. [10] R.J. Gibbens, F.B. Kelly, P.B. Key. A Decision-Theoretic Approach to Call Admission Control in ATM Networks, IEEE Journal on Selected Areas on Communications, vol 13, No 6, August 1995, pp 1101-1113. [11] The cdma2000 ITU-R Candidate Submission, April 1998. [12] OPNET, Modeler Manuals - Modeling, vol 1 & 2, version 6.
