Ioannis D. Moscholios

Connection-dependent threshold model: a generalization of the Erlang multiple rate loss model

In this paper first, we review two extensions of the Erlang multi-rate loss model (EMLM), whereby we can assess the call-level quality-of-service (QoS) of ATM networks. The call-level QoS assessment in ATM networks remains an open issue, due to the emerged elastic services. We consider the coexistence of ABR service with QoS guarantee services in a VP link and evaluate the call blocking probability (CBP), based on the EMLM extensions. In the first extension, the retry models, blocked calls can retry with reduced resource requirements and increased arbitrary mean residency requirements. In the second extension, the threshold models, for blocking avoidance, calls can attempt to connect with other than the initial resource and residency requirements which are state dependent. Secondly, we propose the connection-dependent threshold model (CDTM), which resembles the threshold models, but the state dependency is individualized among call-connections. The proposed CDTM not only generalizes the existing threshold models but also covers the EMLM and the retry models by selecting properly the threshold parameters. Thirdly, we provide formulas for CBP calculation that incorporate bandwidth/trunk reservation schemes, whereby we can balance the grade-of-service among the service-classes. Finally, we investigate the effectiveness of the models applicability on ABR service at call set-up. The retry models can hardly model the behavior of ABR service, while the threshold models perform better than the retry models. The CDTM performs much better than the threshold models; therefore we propose it for assessing the call-level performance of ABR service. We evaluate the above-mentioned models by comparing each other according to the resultant CBP in ATM networks. For the models validation, results obtained by the analytical models are compared with simulation results.

Performance Analysis of OCDMA PONs Supporting Multi-Rate Bursty Traffic

Optical Code Division Multiple Access (OCDMA) provides increased security communications with large dedicated bandwidth to end users and simplified network control. We analyse the call-level performance of an OCDMA Passive Optical Network (PON) configuration, which accommodates multiple service-classes with finite traffic source population. The considered user activity is in accordance with the bursty nature of traffic, so that calls may alternate between active (steady transmission of a burst) and passive states (no transmission at all). Parameters related to multiple access interference, additive noise, user activity and number of traffic sources are incorporated to our analysis, which is based on a two-dimensional Markov chain. An approximate recursive formula is derived for efficient calculation of call blocking probability. Furthermore, we determine the burst blocking probability; burst blocking occurs when a burst delays its returning from passive to active state. The accuracy of the model is completely satisfactory and is verified through simulation. Moreover, we reveal the consistency and necessity of the proposed model.

Call-Level Performance Modelling of Elastic and Adaptive Service-Classes with Finite Population

The call-level performance modelling is a challenge in the highly heterogeneous environment of modern telecom networks, due to the presence of elastic traffic. In this paper, we review existing teletraffic loss models and propose a model for elastic traffic of service-classes with finite population (quasi-random call arrival process). Upon arrival, calls have contingency alternative bandwidth requirements that depend on thresholds which indicate the available/occupied link bandwidth (state dependent model). Calls are admitted under the complete sharing policy, and can tolerate bandwidth compression, while in-service. We prove a recurrent formula for the efficient calculation of the link occupancy distribution and consequently the call blocking probabilities and link utilization. The accuracy of the proposed model is verified by simulation and is found to be quite satisfactory. Comparative results with other existing models show the necessity and the effectiveness of the proposed model. Its potential applications are mainly in the environment of wireless networks.

Congestion probabilities in a batched Poisson multirate loss model supporting elastic and adaptive traffic

The ever increasing demand of elastic and adaptive services, where in-service calls can tolerate bandwidth compression/expansion, together with the bursty nature of traffic, necessitates a proper teletraffic loss model which can contribute to the call-level performance evaluation of modern communication networks. In this paper, we propose a multirate loss model that supports elastic and adaptive traffic, under the assumption that calls arrive in a single link according to a batched Poisson process (a more “bursty” process than the Poisson process, where calls arrive in batches). We assume a general batch size distribution and the partial batch blocking discipline, whereby one or more calls of a new batch are blocked and lost, depending on the available bandwidth of the link. The proposed model does not have a product form solution, and therefore we propose approximate but recursive formulas for the efficient calculation of time and call congestion probabilities, link utilization, average number of calls in the system, and average bandwidth allocated to calls. The consistency and the accuracy of the model are verified through simulation and found to be quite satisfactory.

Call-burst blocking of ON-OFF traffic sources with retrials under the complete sharing policy

In this paper we calculate both call and burst blocking probabilities of ON-OFF traffic sources with retrials. Calls of service-classes arrive to a single link according to a Poisson process and compete for the available link bandwidth under the complete sharing policy. Blocked calls may immediately retry one or more times to enter the system, with reduced bandwidth and increased mean service time requirements. Call blocking occurs when a call cannot enter the system with its last bandwidth requirement, due to lack of bandwidth. Accepted calls enter the system via state ON and may alternate between states ON and OFF, or remain always in state ON. When a call is transferred to state OFF it releases the bandwidth held in state ON, so that this bandwidth becomes available to new arriving calls. When a call tries to return to state ON, it re-requests its bandwidth. If it is available a new ON-period (burst) begins. Otherwise burst blocking occurs and the call remains in state OFF. The proposed ON-OFF retry models do not have a product form solution and therefore the calculation of call and burst blocking probability is based on approximate formulas. The formulas we propose for the call blocking probabilities are recursive, whereas for the burst blocking probabilities are robust. Simulation results validate our analytical methodology. For further evaluation, the results of the ON-OFF retry models are compared with those of the ON-OFF model without retrials. We also discuss the extension of the proposed formulas in the case of a fixed-routing network.

An Analytical Approach for Dynamic Wavelength Allocation in WDM–TDMA PONs Servicing ON–OFF Traffic

Optical access systems are now considered a feasible alternative to the predominant broadband access technologies, while, at the same time, passive optical networks (PONs) are viewed as an attractive and promising type of fiber access system. In this paper we present and analyze three basic dynamic wavelength allocation scenarios for a hybrid wavelength division multiplexing-time division multiple access (WDM-TDMA) PON. We propose new teletraffic loss models for calculating call-level performance measures, like connection failure probabilities (due to unavailability of a wavelength) and call blocking probabilities (due to the restricted bandwidth capacity of a wavelength). The PON accommodates bursty service-classes of ON-OFF traffic. The proposed models are extracted from one-dimensional Markov chains, which describe the wavelength occupancy in the PON, and two-dimensional Markov chains, which describe the bandwidth occupancy inside a wavelength. The accuracy of the proposed models is validated through simulation and is found to be quite satisfactory. Moreover, these models are computationally efficient because they are based on recursive formulas.

Performance metrics of a multirate resource sharing teletraffic model with finite sources under the threshold and bandwidth reservation policies

The authors propose a new multirate teletraffic loss model of a single link with certain capacity that accommodates different service-classes whose calls come from finite traffic sources. Calls compete for the available link bandwidth under the combination of the threshold (TH) and the bandwidth reservation (BR) policies. The TH policy can provide different quality of service among service-classes by limiting calls of each service-class up to a certain number, which is a predefined TH, which can be different for each service-class. The BR policy reserves part of the available link bandwidth to benefit calls of high bandwidth requirements. They show that the proposed model, without the BR policy, has a product form solution (PFS) and prove recursive formulas for the efficient calculation of the call-level performance metrics, such as time and call congestion probabilities as well as link utilisation. The combination of the TH and BR policies destroys the PFS of the model. However, they show that approximate but recursive formulas still exist for the efficient calculation of the call-level performance metrics. The accuracy of the proposed formulas is verified through simulation and found to be very satisfactory.

QoS guarantee in a batched poisson multirate loss model supporting elastic and adaptive traffic

In this paper, we consider a single link that supports both elastic and adaptive traffic of Batch Poisson arriving calls, under the Bandwidth Reservation (BR) policy, whereby we can achieve specific QoS per service-class. Arriving batches have a generally distributed batch size, and can be serviced either as a whole or in part (partial batch blocking discipline), depending on the available link bandwidth. Blocked calls are lost. Accepted calls of a batch can compress or expand their bandwidth; elastic calls expand or compress their service time accordingly, while adaptive calls do not alter their service time. This system does not have a Product Form Solution. For the efficient calculation of time and call congestion probabilities as well as link utilization, we derive approximate but recursive formulas. The accuracy of the model is completely satisfactory and is verified together with the models consistency, through simulation. Comparison of the new model with existing models reveals its necessity.

Congestion probabilities of elastic and adaptive calls in Erlang-Engset multirate loss models under the threshold and bandwidth reservation policies

In this paper, we consider a single link of fixed capacity that accommodates calls of different service-classes with different bandwidth-per-call requirements. The link behaves as a multirate loss system. Calls of each service-class arrive in the link according to a Poisson (random) or a quasi-random process and have an exponentially distributed service time. Poisson or quasi-random arriving calls are generated by an infinite or finite number of traffic sources, respectively. Service-classes are also distinguished according to the behavior of in-service calls, in elastic and adaptive service-classes. Elastic calls can compress their bandwidth by simultaneously increasing their service time. Adaptive calls tolerate bandwidth compression without affecting their service time. All calls compete for the available link bandwidth under the combination of the Threshold (TH) and the Bandwidth Reservation (BR) policies. The TH policy can provide different QoS among service-classes by limiting the number of calls of a service-class up to a predefined threshold, which can be different for each service-class. The BR policy reserves part of the available link bandwidth to benefit calls of high bandwidth requirements. The proposed models, for random or quasi-random traffic, do not have a product form solution for the determination of the steady state probabilities. However, we approximate both models by reversible Markov chains, and prove recursive formulas for the efficient calculation of the call-level performance metrics, such as time and call congestion probabilities as well as link utilization. The accuracy of the proposed formulas is verified through simulation and found to be quite satisfactory.

The extended connection-dependent threshold model for call-level performance analysis of multi-rate loss systems under the bandwidth reservation policy

Firstly, we reviewed two extensions of the Erlang multi-rate loss model, whereby we can assess the call-level QoS of telecom networks supporting elastic traffic: (i) the extended Erlang multi-rate loss model, where random arriving calls of certain bandwidth requirements at call setup can tolerate bandwidth compression while in service; and (ii) the connection-dependent threshold model, where arriving calls may have several contingency bandwidth requirements, whereas in-service calls cannot tolerate bandwidth compression. Secondly, we proposed a new model, the extended connection-dependent threshold model. Calls may have alternative bandwidth requirements at call setup and can tolerate bandwidth compression while in service. We proposed a recurrent formula for the efficient calculation of link occupancy distribution and consequently call blocking probabilities, link utilization, and throughput per service class. Furthermore, in the proposed model, we incorporated the bandwidth reservation policy, whereby we can (i) equalize the call blocking probabilities of different service classes, (ii) guarantee specific QoS per service class, and (iii) implement different maximum bandwidth compression/expansion rate per service class so that the network supports both elastic and stream traffic. The accuracy of the new model is verified by simulation. Moreover, the proposed model performs better than the existing models. Finally, we generalize the proposed model by incorporating service classes with either random or quasi-random arrivals. Copyright