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16.5 ANALYTICAL MODEL FOR ORDINARY NODE IN CLUSTER WITH SKKE In this section we will develop a Markov chain model for node behavior that includes all phases of the SKKE protocol and subsequent sleep and transmission phases. We assume that the PAN coordinator maintains a separate counter for the number of transmissions by each node. When counter value reaches threshold nk, key update protocol is triggered. Updated keys are used to generate message authentication code. The high level Markov chain, which includes key update sleep periods followed by the transmissions, is presented in Fig. 16.6. Furthermore, each of the steps that involves downlink transmission requires synchronization with the beacon, transmission of the uplink request packet, and transmission of the downlink packet as shown in Fig. 16.2b. Every transmission is implemented using slotted CSMA/CA speci ed by the standard [1]. Markov subchain for single CSMA/CA transmission (as the component of the Fig. 16.6) is shown in Fig. 16.7. The delay line from Fig. 16.7 models the requirement from the standard that every transmission that cannot be fully completed within the current superframe has to be delayed to the beginning of the next superframe and is shown in Fig. 16.8a. The probability that a packet will be delayed is denoted as Pd Dd =SD where SD denotes duration of active superframe part (in backoff periods) and Dd 2 Gp 1 Ga denotes total packet transmission time including two clear channel assessments, transmission time Gp , waiting time for the acknowledgment, and acknowledgment transmission time Ga . The block labeled Tr denotes Dd linearly connected backoff periods needed for actual transmission. Within the transmission subchain, the process {i,c,k,d} de nes the state of the device at backoff unit boundaries where iA(0..m) is the index of current

You can see how the certainty changes with the various percents of noise..

that it has no data to transmit and there is no data to be transmitted from any neighbor to it for some duration in the future, it can go to sleep. Instead of reserving slot(s) of one level for the use of another level, another approach is to use multiple channels, one for each level. In the above example, level 2 can use a channel that is different from that of level 1; and the bandwidth of the channel used by level 2 can be much smaller than that used by level 1.

When a user starts browsing, he/she accesses the homepage (by default) and then traverses the Web site under study Given the structure of this Web site, we expect few sessions access only one page, since during these sessions users only connect but do not browse Thus, if we choose a very small session inactivity period, many accesses will be incorrectly counted as part of separate single-hit sessions As the session inactivity period increases, these accesses are correctly classi ed as part of larger sessions and the number of single-hit sessions will decrease The appropriate session inactivity period is at the knee point where the change in its value does not produce a signi cant change in the number of single-hit sessions Figure 512 shows the number of single-hit sessions versus the session inactivity period.

use of psychotropic medication, electroconvulsive therapy (ECT), and biofeedback or social interventions such as large-scale community education programs, structured residential communities (e.g., halfway houses), and various types of prevention programs. Nonpsychotherapy treatment and prevention interventions may be used in addition to psychotherapy or without psychotherapy. For example, a patient may routinely take an antidepressant medication such as Prozac or an antianxiety agent such as Xanax with or without participating in psychotherapy. The medications might be provided by a trained mental health professional such as a psychiatrist or by someone with minimal mental health training such as an internal medicine or family practice physician. A clinician might use bio-feedback with or without psychotherapy to treat a range of problems such as anxiety, phobia, headaches, or irritable bowel syndrome. Finally, a patient may enroll in a halfway house for substance abuse with or

The gure shows that the knee point occurs somewhere between 30 and 45 seconds; we use this knee point as the session inactivity period Note that even though our analysis is based on correctly classifying single-hit sessions, it impacts the classi cation of multihit sessions as well We can verify our chosen period in another manner As the session inactivity period increases, smaller sessions merge into larger ones, thereby decreasing the total number of sessions, until all sessions are merged into one big session There is a point at which the rate of decrease of sessions becomes relatively steady and low Again, this occurs in the region where the real session inactivity period lies In Figure 512, there is a relatively steep drop in the number of sessions from 10 to 30 seconds and then a smoother curve from 30 seconds onward is observed.

This analysis con rms the fact that the session inactivity period lies in the range from 30 to 45 seconds This value is different from the one reported by Kunz et al [21], who used 90 seconds as the threshold for reclaiming dynamic IP addresses..

The total amount of time it takes to set up a call, measured from the moment the last digit of the rst-stage dial-in number as in multistage dialing is entered to the moment the ring-back tone is heard at the calloriginating side. In IP telephony, call setup time can vary from 500 msec to 10 sec, depending on the availability of network and digital signal processing (DSP) resources in the system being used. This refers to the call setup time in an idle system. I discuss these and related issues in Appendix A. The number of simultaneous calls that can be handled without any precall wait. This refers to setting up a call in a busy system. Note that the precall wait can vary from as little as 1 sec to as much as 10 sec, depending on the speed of the CPU used in the IP-PSTN GW, availability of memory/ storage and (digital signal) processing resources in the system, and so on. I discuss these and related issues in Appendix B.

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