We propose a simple approximate model for unslotted opportunistic spectrum access networks under nonsaturation conditions. The main simplification we introduce is that all secondary users, except a tagged one, in nonsaturated setting can be approximated by saturated ones with a scaled version of backoff interval. We analyze the approximate model and verify the model using simulations.

We investigate delay analysis of multi-hop wireless mesh network (WMN) where nodes have multi-channel and multiple transceivers to increase the network capacity. The functionality of the multi-channel and multiple transceivers allows the whole WMN to be decomposed into disjoint zones in such a way that i) nodes in a zone are within one-hop distance, and relay node and end nodes with different CWmins contend to access the channel based on IEEE 802.11e EDCA, ii) different channels are assigned to neighbor zones to prevent the hidden node problem, iii) relay nodes can transmit and receive the packets simultaneously by multi-channel and multiple transceivers. With this decomposition of the network, we focus on the delay at a single zone and then the end-to-end delay can be obtained as the sum of zone-delays. In order to have the location-independent end-to-end delay to the gateway regardless of source nodes' locations, we propose two packet management schemes, called the differentiated CW policy and the strict priority policy, at each relay node where relay packets with longer hop count are buffered in higher priority queues according to their experienced hop count. For the differentiated CW policy, a relay node adopts the functionality of IEEE 802.11e EDCA where a higher priority queue has a shorter minimum contention window. We model a typical zone as a one-hop IEEE 802.11e EDCA network under non-saturation condition where priority queues have different packet arrival rates and different minimum contention window sizes. First, we find the PGF (probability generating function) of the HoL-delay of packets at priority queues in a zone. Second, by modeling each queue as M/G/1 queue with the HoL-delay as a service time, we obtain the packet delay (the sum of the queueing delay and the HoL-delay) of each priority queue in a zone. Third, the average end-to-end delay of packet generated at end node in each zone is obtained by summing up the packet delays at each zone. For the strict priority policy, we regard a relay node as a single queueing system with multiple priority queues where relay packets in priority queues are served in the order of strict priority. Relay node has smaller CWmin than end node has and relay node competes with end nodes in a zone. Using the PGF of HoL-delay of packet at relay node and end node, we obtain the packet delay in a zone. The average end-to-end delay to the gateway generated at end node in each zone is obtained. Finally, for both the differentiated CW policy and strict priority policy, by equating all end-to-end delays to be approximately equal, we find the minimum contention window sizes of each priority queue numerically by trial and error method so that end-to-end delays of packets are almost equal regardless of their source's location, respectively. Numerical results show that proposed two methods obtain almost same end-to-end delay of packets regardless of their generated locations and our analytical results are shown to be well matched with the simulation results.

The IEEE 802.16e standard specifies the sleep mode and the idle mode of a mobile station (MS) for power saving. In this paper, to reduce the energy consumption of the MS, we employ the sleep mode while the MS is on-session, and the idle mode while it is off-session. Under the assumption that the time duration from the end of a session to the arrival of a new downlink session request follows an exponential distribution of the mean and that arrivals of messages during an on-session follow a Poisson process with rate λ, we analyze the awake mode period and the sleep mode period by using the busy period analysis of the M/G/1 queue, and then we derive the total mean length of an on-session which consists of a geometric number of awake mode periods and sleep mode periods. Since the sum of an on-session and an off-session constitutes a cycle, we can express the average power consumption in terms of the mean lengths of an awake mode period, a sleep mode period and an idle mode period. The average power consumption indicates how much the MS can save energy by employing the sleep mode and the idle mode. We also derive the Laplace Stieltjes transform (and the mean) of the queueing delay of messages to examine a tradeoff between the power consumption and the delay of messages. Analytical results, which are shown to be well-matched by simulations, address that our employment of the sleep mode and the idle mode provides a considerable reduction in the energy consumption of the MS.

Recent improvements in the performance of end-computers and networks have made it feasible to construct a grid system over the Internet. A grid environment consists of many computers, each having a set of components and a distinct performance. These computers are shared among many users and managed in a distributed manner. Thus, it is important to focus on a situation in which the computers are used unevenly due to decentralized management by different task schedulers. In this study, which is a preliminary investigation of the performance of task allocation schemes employed in a decentralized environment, the average execution time of a long-lived task is analytically derived using the M/G/1-PS queue. Furthermore, assuming a more realistic condition, we evaluate the performance of some task allocation schemes adopted in the analysis, and clarify which scheme is applicable to a realistic grid environment.

In this paper, we propose an algorithm to calculate the higher moments of the busy period length of a discrete-time M/G/1 type queue with finite buffer. The queueing model has a level-dependent transition probability matrix. Our algorithm is given as a set of recursive formulas which are derived from the relationship among the generating function matrices of the fundamental period. As an example of our algorithm, we provide an approximate analysis of a HOL (Head Of Line) priority control queue.

This paper presents a finite buffer M/G/1 queue with two classes of customers who are served by a combination of head-of-the-line priority and buffer reservation schemes. This combination gives each class of customers high or low priorities in terms of both delay and loss. The scheme is analyzed for the model in which one class of customers has high priorities over the other class of customers with respect to both delay and loss. First, steady-state joint probability distribution of the number of each class of customers in the buffer and remaining service time is derived by a supplementary variable method. Second, loss probability and mean waiting time for each class of customers are provided using this probability distribution. Finally, a combination of head-of-the-line priority and buffer reservation schemes is numerically compared with other buffer management schemes in terms of admissible offered load to show its effectiveness under differing QoS requirements.

This paper analyzes a finite buffer M/G/1 queue with two classes of customers who are served by a combination of head-of-the-line priority and push-out schemes. This combination gives each class of customers two different types of priorities with respect to both delay and loss. There are two models considered. The first one is that one class of customers has a higher priority over the other class with respect to both delay and loss; the second one is that one class has a higher priority with respect to loss and the other has high-priority with respect to delay. For both of these models, the joint probability distribution of the number of customers of both classes in the buffer is derived by a supplementary variable method. Using this probability distribution, we can easily calculate the loss probabilities of both classes, the mean waiting time for high-priority customers with respect to loss and the upper bound for mean waiting time for low-priority customers with respect to loss. Numerical examples demonstrate an effect of the combination of different types of priorities.

In this paper, we derive the mean message waiting times in a local area network that uses the Demand-Priority Access Method. We model the system as a two-priority M/G/1 queue with switchover time between service periods. This switchover time accounts for the polling and port selection performed by the repeater after each message transmission. The service discipline is non-preemptive and the length of the switchover time is dependent upon the priority class of the preceding message served as well as that of the message to be served next. The dependency in the switchover times is motivated by the polling and port selection operation of the protocol and it makes the analysis much more involved. In order to avoid the complexities of an exact analysis, we make some independence assumptions and thus obtain an approximate solution. Laplace-Stieltjes transforms of the stationary probability distribution functions for the waiting time of high- and normal-priority messages are derived, and subsequently, the expressions for the mean message waiting times. Numerical results computed using these expressions are verified using simulations which model the actual protocol. These numerical results which are shown to be accurate can be easily computed with widely available mathematical software.

Let TBP be the server busy period of an M/G/1 queueing system characterized by arrival intensity λ and service time c.d.f. A(τ). In this paper, we investigate the regularity structure of the Laplace transform σBP(s)=E[] on the complex s-plane. It is shown, under certain broad conditions, that finite singular points of σBP(s) are all branch points. Furthermore the branch point s0 having the greatest real part is always purely negative and is of multiplicity two. The basic branch point s0 and the associated complex structure provide a basis for an asymptotic representation of various descriptive distributions of interest. For a natural relaxation time |s0|-1 of the M/G/1 system, some useful bounds are obtained and the asymptotic behavior as traffic intensity approaches one is also discussed. Detailed results of engineering value are provided for two important classes of service time distributions, the completely monotone class and the Erlang class.