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An analytical model for performance evaluation of multimedia applications over EDCA in an IEEE 802.11e WLAN

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Abstract

We extend the modeling heuristic of (Harsha et al. 2006. In IEEE IWQoS ’06, pp 178 – 187) to evaluate the performance of an IEEE 802.11e infrastructure network carrying packet telephone calls, streaming video sessions and TCP controlled file downloads, using Enhanced Distributed Channel Access (EDCA). We identify the time boundaries of activities on the channel (called channel slot boundaries) and derive a Markov Renewal Process of the contending nodes on these epochs. This is achieved by the use of attempt probabilities of the contending nodes as those obtained from the saturation fixed point analysis of (Ramaiyan et al. 2005. In Proceedings ACM Sigmetrics, ’05. Journal version accepted for publication in IEEE TON). Regenerative analysis on this MRP yields the desired steady state performance measures. We then use the MRP model to develop an effective bandwidth approach for obtaining a bound on the size of the buffer required at the video queue of the AP, such that the streaming video packet loss probability is kept to less than 1%. The results obtained match well with simulations using the network simulator, ns-2. We find that, with the default IEEE 802.11e EDCA parameters for access categories AC 1, AC 2 and AC 3, the voice call capacity decreases if even one streaming video session and one TCP file download are initiated by some wireless station. Subsequently, reducing the voice calls increases the video downlink stream throughput by 0.38 Mbps and file download capacity by 0.14 Mbps, for every voice call (for the 11 Mbps PHY). We find that a buffer size of 75KB is sufficient to ensure that the video packet loss probability at the QAP is within 1%.

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Notes

  1. The basic access mechanism is one of the two access mechanisms based on the CSMA/CA (carrier sense multiple access/collision avoidance) protocol for wireless transmissions. The other is the RTS/CTS (request to send/ clear to send) mechanism. See [23] for details.

  2. The only change will be the values of various possible channel slot lengths, L j ;j ≥ 0, due to the differences in packet transmission times.

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Acknowledgment

This work is based on research sponsored by Intel Technology, India.

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Authors and Affiliations

  1. Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, 560012, India

    Sri Harsha, Anurag Kumar & Vinod Sharma

Authors
  1. Sri Harsha
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  2. Anurag Kumar
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  3. Vinod Sharma
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Corresponding author

Correspondence to Anurag Kumar.

Additional information

This is an extended version of our paper (Harsha et al. 2006. An analytical model for the capacity estimation of combined VoIP and TCP file transfers over EDCA in an IEEE 802.11e WLAN, pp. 178–187, 19–21 June 2006) in IEEE IWQoS ’06.

Appendices

Appendices

1.1 Appendix A: Expressions for various probability functions (defined in 3.2)

Define

$$ \tau^{(.)} := \beta_{Y_j^{(v)}+1,1,Y_j^{(t)}+1}^{(.)} $$

Then,

$$ \eta_v (Y_j^{(v)}, Y_j^{(t)}) =(1-\tau^{(v)})^{Y_j^{(v)}+1} $$
$$ \eta_{vd} (Y_j^{(v)}, Y_j^{(t)})=(1-\tau^{(vd)}) $$
$$ \eta_t (Y_j^{(v)}, Y_j^{(t)}) =(1-\tau^{(t)})^{Y_j^{(t)}+1} $$
$$ \alpha_v (Y_j^{(v)}, Y_j^{(t)}) = Y_j^{(v)}\frac{\tau^{(v)}\eta_v (Y_j^{(v)} , Y_j^{(t)})}{1-\tau^{(v)}} $$
$$ \alpha_t (Y_j^{(v)}, Y_j^{(t)}) = Y_j^{(t)}\frac{\tau^{(t)}\eta_t (Y_j^{(v)} , Y_j^{(t)})}{1-\tau^{(t)}} $$
$$ \sigma_v (Y_j^{(v)}, Y_j^{(t)})= \frac{\alpha_v (Y_j^{(v)}, Y_j^{(t)})}{Y_j^{(v)}} $$
$$ \sigma_{vd} (Y_j^{(v)}, Y_j^{(t)}) = 1-\eta_{vd} (Y_j^{(v)} , Y_j^{(t)}) $$
$$ \sigma_t (Y_j^{(v)}, Y_j^{(t)}) = \frac{\alpha_t (Y_j^{(v)} , Y_j^{(t)})}{Y_j^{(t)}} $$
$$ \zeta_v (Y_j^{(v)}, Y_j^{(t)})= \sum^{Y_j^{(v)}+1}_{i=2}\frac{\left(\begin{array}{c}Y_j^{(v)}+1\\ {i}\end{array}\right)(\tau^{(v)})^i\eta_v (Y_j^{(v)} , Y_j^{(t)})}{(1-{\tau^{(v)}})^i} $$
$$ \zeta_t (Y_j^{(v)} , Y_j^{(t)}) = \sum^{Y_j^{(t)}}_{i=2}\frac{\left(\begin{array}{c} Y_j^{(t)}\\i\end{array}\right)(\tau^{(t)})^i\eta_t (Y_j^{(v)} , Y_j^{(t)})}{(1-{\tau^{(v)}})^i} $$
$$ \begin{aligned} \psi_{v-tsta} (Y_j^{(v)} , Y_j^{(t)}) =& \sum^{Y_j^{(v)}+1}_{i=1}\frac{\left(\begin{array}{c}Y_j^{(v)}+1\\ {i}\end{array}\right) (\tau^{(v)})^i\eta_v (Y_j^{(v)} , Y_j^{(t)})}{(1-{\tau^{(v)}})^i} \\ &\sum^{Y_j^{(t)}}_{i=1}\frac{\left(\begin{array}{c}Y_j^{(t)}\\ {i}\end{array}\right) (\tau^{(t)})^i\eta_t (Y_j^{(v)} , Y_j^{(t)})}{(1-{\tau^{(t)}})^i} \end{aligned} $$
$$ \begin{aligned} \psi_{v-vd} (Y_j^{(t)} , Y_j^{(t)}) =&\sigma_{vd} (Y_j^{(v)} , Y_j^{(t)})\\& \sum^{Y_j^{(t)}}_{i=1}\frac{\left(\begin{array}{c}Y_j^{(t)}\\ {i}\end{array}\right)(\tau^{(t)})^i\eta_t (Y_j^{(v)} , Y_j^{(t)})}{(1-{\tau^{(t)}})^i} \end{aligned} $$
$$ \begin{aligned} \psi_{vdAP} (Y_j^{(v)} , Y_j^{(t)})=& \sigma_{vd} (Y_j^{(v)} , Y_j^{(t)}) \left [\eta_t (Y_j^{(v)}, Y_j^{(t)}) \right. &\sum^{Y_j^{(v)}+1}_{i=1}\frac{\left(\begin{array}{c}Y_j^{(v)}+1\\ {i}\end{array}\right)(\tau^{(v)})^i\eta_v (Y_j^{(v)} , Y_j^{(t)})}{(1-{\tau^{(v)}})^i} \\ +& \eta_{v} (Y_j^{(v)} , Y_j^{(t)}) &\sum^{Y_j^{(t)}}_{i=1}\frac{\left(\begin{array}{c}Y_j^{(t)}\\ {i}\end{array}\right)(\tau^{(t)})^i\eta_t (Y_j^{(v)} , Y_j^{(t)})}{(1-{\tau^{(t)}})^i} \\ +&\left.\psi_{v-tsta} (Y_j^{(v)} , Y_j^{(t)}) \right ] \end{aligned} $$
$$\begin{aligned} \psi_{tAP} (Y_j^{(v)} , Y_j^{(t)}) = \tau^{(t)} \left [\frac{\eta_{vd} (Y_j^{(v)} , Y_j^{(t)})\eta_t (Y_j^{(v)}, Y_j^{(t)})}{(1-\tau^{(t)})}\right. &\sum^{Y_j^{(v)}+1}_{i=1}\frac{\left(\begin{array}{c}Y_j^{(v)}+1\\{i}\end{array}\right)(\tau^{(v)})^i\eta_v (Y_j^{(v)} , Y_j^{(t)})} {(1-{\tau^{(v)}})^i}\\ +& \eta_{v} (Y_j^{(v)} , Y_j^{(t)})\eta_{vd} (Y_j^{(v)} , Y_j^{(t)}) \sum^{Y_j^{(t)}}_{i=1}\frac{\left(\begin{array}{c}Y_j^{(t)}\\ {i}\end{array}\right)(\tau^{(t)})^i\eta_t (Y_j^{(v)} , Y_j^{(t)})} {(1-{\tau^{(t)}})^i} \\ +&\psi_{v-tsta} (Y_j^{(v)} , Y_j^{(t)})\eta_{vd} (Y_j^{(v)} , Y_j^{(t)}) \\ +& \frac{\eta_t (Y_j^{(v)}, Y_j^{(t)})}{(1-\tau^{(t)})}\psi_{v-vd} (Y_j^{(v)} , Y_j^{(t)})\\ +&\sigma_{vd} (Y_j^{(v)} , Y_j^{(t)})\psi_{v-tsta} (Y_j^{(v)} , Y_j^{(t)})\\ +& \sigma_{vd} (Y_j^{(v)} , Y_j^{(t)})\eta_{v} (Y_j^{(v)} , Y_j^{(t)})\\ &\left.\sum^{Y_j^{(t)}}_{i=1}\frac{\left(\begin{array}{c}Y_j^{(t)}\\ {i}\end{array}\right)(\tau^{(t)})^i\eta_t (Y_j^{(v)} , Y_j^{(t)})}{(1-{\tau^{(t)}})^i} \right ] \end{aligned} $$

Note that all the probability functions are denoted as functions of \(Y_j^{(v)}\) and \(Y_j^{(t)}\) even when one of them may not be there in the expression, since β and hence τ is a function of both \(Y_j^{(v)}\) and \(Y_j^{(t)}.\)

1.2 Appendix B: Numerical calculation of stationary distribution (refers to Sect. 3.2)

The transition probability matrix can be numerically generated using the above probability functions and distributions of arrivals of VoIP packets. For instance, consider N v  = 5, N t  = 10 and N vd  = 1. Let \((Y_j^{(v)} , Y_j^{(t)}, C_j)=(3,2,0)\) be the state of the Markov chain \(\{Y_j^{(v)},Y_j^{(t)},C_j; j{\geq}0 \}\) at the end of jth channel slot. Then all three types of AC categories can contend in the next channel slot, implying that QAP v , QAP vd , QAP t , 3 QSTA v s and 2 QSTA t s may contend for the channel in the (j + 1)th channel slot.

Now let C j+1 = 0. This implies that an idle slot has occurred because none of the nodes contended for the channel. Then the number of contending QSTA t s does not change. The number of contending QSTA v s cannot decrease, but may increase by at most 2 (due to new arrival of packets). Then the state at (j + 1)th channel slot boundary can be one of the 3 states : (3,2,0), if no VoIP packet arrives, (4,2,0), if one VoIP packet arrives, and (5,2,0), if 2 VoIP packets arrive. Then the transitional probabilities are as under:

$$ \begin{aligned} Pr&((3,2,0)|(3,2,0))=\eta_v (Y_j^{(v)} , Y_j^{(t)})\eta_t (Y_j^{(v)} , Y_j^{(t)})\\ &\eta_{vd} (Y_j^{(v)} , Y_j^{(t)})Pr \left(B_{j+1}^{(v)} = 0 |(Y_j^{(v)} =3;L_{j+1}=\delta)\right) \end{aligned} $$
$$ \begin{aligned} Pr&((4,2,0)|(3,2,0))=\eta_v (Y_j^{(v)} , Y_j^{(t)})\eta_t (Y_j^{(v)} , Y_j^{(t)})\\ &\eta_{vd} (Y_j^{(v)} , Y_j^{(t)})Pr \left(B_{j+1}^{(v)} = 1 |(Y_j^{(v)} =3;L_{j+1}=\delta)\right) \end{aligned} $$
$$ \begin{aligned} Pr&((5,2,0)|(3,2,0))=\eta_v (Y_j^{(v)} , Y_j^{(t)}) \eta_t (Y_j^{(v)} , Y_j^{(t)})\\ &\eta_{vd} (Y_j^{(v)} , Y_j^{(t)})Pr\left(B_{j+1}^{(v)} = 2 |(Y_j^{(v)} =3;L_{j+1}=\delta)\right) \end{aligned} $$

Instead, if C j+1 = 1, then this implies that an activity has occurred in the channel and that could have been either a successful transmission by one of the contending nodes or there has been collision between two or more contending nodes. Then the next states could be one of the these 10 states: (2,2,1) if QSTA v succeeded and no VoIP packet arrived; (3,2,1) if collision took place and no VoIP packet arrived or QAP v succeeded and no VoIP packet arrived or QAP vd succeeded and no VoIP packet arrived or QSTA v succeeded and 1 VoIP packet arrived; (4,2,1) if collision took place and 1 VoIP packet arrived or QAP v succeeded and 1 VoIP packet arrived or QAP vd succeeded and 1 VoIP packet arrived or QSTA v succeeded and 2 VoIP packets arrived; (5,2,1) if collision took place and 2 VoIP packets arrived or QAP v succeeded and 2 VoIP packets arrived or QAP vd succeeded and 2 VoIP packets arrived; (3,3,1) if QAP t succeeded and no VoIP packet arrived; (4,3,1) if QAP t succeeded and 1 VoIP packet arrived; (5,3,1) if QAP t succeeded and 2 VoIP packets arrived; (3,1,1) if QSTA t succeeded and no VoIP packet arrived; (4,1,1) if QSTA t succeeded and 1 VoIP packet arrived; and (5,1,1) if QSTA t succeeded and 2 VoIP packets arrived. The transition probabilities for these transitions can similarly be written (as for C j+1 = 0 case) using the probability functions and conditional probability function of VoIP packet arrivals.

Thus the transition probability matrix can be numerically worked out and then, combining with \(\sum_{n_v=0}^{N_v}\sum_{n_t=0}^{N_t}\sum_{c=0}^{1}\pi_{n_v,n_t,c}=1,\) the stationary distribution \(\varvec{\pi}\) of the Markov chain \(\{Y_j^{(v)},Y_j^{(t)},C_j; j{\geq}0 \}\) can be evaluated.

1.3 Appendix C: Mean cycle length, L j (refers to Sect. 3.3)

$$ \begin{aligned} {\mathsf{E}}L_{j+1}|(C_j = 0)=& \eta_v (Y_j^{(v)} , Y_j^{(t)})\eta_t (Y_j^{(v)} , Y_j^{(t)})\eta_{vd} (Y_j^{(v)} , Y_j^{(t)}) \\ +& T_{s-v} \eta_t (Y_j^{(v)} , Y_j^{(t)}) \eta_{vd} (Y_j^{(v)} , Y_j^{(t)})\left((\alpha_v (Y_j^{(v)} , Y_j^{(t)})\right.\\ &\left.+ \sigma_v (Y_j^{(v)} , Y_j^{(t)})\right) \\ +& T_{s-vdAP} \eta_v (Y_j^{(v)} , Y_j^{(t)})\eta_{t} (Y_j^{(v)} , Y_j^{(t)}) \sigma_{vd} (Y_j^{(v)} , Y_j^{(t)})\\ +& T_{s-tAP} \eta_v (Y_j^{(v)} , Y_j^{(t)})\eta_{vd} (Y_j^{(v)} , Y_j^{(t)}) \sigma_t (Y_j^{(v)} , Y_j^{(t)}) \\ +& T_{s-tSTA} \eta_v (Y_j^{(v)} , Y_j^{(t)})\eta_{vd} (Y_j^{(v)} , Y_j^{(t)}) \alpha_t (Y_j^{(v)} , Y_j^{(t)})\\ +& T_{c-short} \eta_v (Y_j^{(v)} , Y_j^{(t)})\eta_{vd} (Y_j^{(v)} , Y_j^{(t)}) \zeta_t (Y_j^{(v)} , Y_j^{(t)}) \\ +& T_{c-voice} \left(\eta_t (Y_j^{(v)} , Y_j^{(t)})\eta_{vd} (Y_j^{(v)} , Y_j^{(t)}) \zeta_v (Y_j^{(v)} , Y_j^{(t)})\right.\\ & \left. + \eta_{vd} (Y_j^{(v)} , Y_j^{(t)})\psi_{v-tsta} (Y_j^{(v)} , Y_j^{(t)})\right) \\ +& T_{c-vd} \psi_{vd-AP}(Y_j^{(v)} , Y_j^{(t)}) \\ +& T_{c-long} \psi_{tAP} (Y_j^{(v)} , Y_j^{(t)}) \end{aligned} $$

and

$$ \begin{aligned} {\mathsf{E}}L_{j+1}|(C_j = 1) =& \eta_v (Y_j^{(v)} , Y_j^{(t)})\eta_{vd} (Y_j^{(v)} , Y_j^{(t)}) \\ +& T_{s-v} \eta_{vd} (Y_j^{(v)} , Y_j^{(t)})(\alpha_v (Y_j^{(v)} , Y_j^{(t)}) + \sigma_v (Y_j^{(v)} , Y_j^{(t)})) \\ +& T_{c-voice} \eta_{vd} (Y_j^{(v)} , Y_j^{(t)})\zeta_v (Y_j^{(v)} , Y_j^{(t)})\\ +& T_{c-vd} \psi_{v-vd}(Y_j^{(v)} , Y_j^{(t)}) \end{aligned} $$

Note that the above Equations use L j in units of system slots.

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Harsha, S., Kumar, A. & Sharma, V. An analytical model for performance evaluation of multimedia applications over EDCA in an IEEE 802.11e WLAN. Wireless Netw 16, 367–385 (2010). https://doi.org/10.1007/s11276-008-0137-y

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