Trunk Reservation Research Articles

Metastability in loss networks with dynamic alternative routing

Consider N stations interconnected with links, each of capacity K, forming a complete graph. Calls arrive to each link at rate λ and depart at rate 1. If a call arrives to a link xy, connecting stations x and y, which is at capacity, then a third station z is chosen uniformly at random and the call is attempted to be routed via z: if both links xz and zy have spare capacity, then the call is held simultaneously on these two; otherwise the call is lost. We analyse an approximation of this model. We show rigorously that there are three phases according to the traffic intensity α:=λ/K: for α∈(0,αc)∪(1,∞), the system has mixing time logarithmic in the number of links n:=N2; for α∈(αc,1) the system has mixing time exponential in n, the number of links. Here αc:=13(5 10−13)≈0.937 is an explicit critical threshold with a simple interpretation. We also consider allowing multiple rerouting attempts. This has little effect on the overall behaviour; it does not remove the metastability phase. Finally, we add trunk reservation: in this, some number σ of circuits are reserved; a rerouting attempt is only accepted if at least σ+1 circuits are available. We show that if σ is chosen sufficiently large, depending only on α, not K or n, then the metastability phase is removed.

On the optimality of a maintenance queueing system

We consider a finite single-server maintenance queue with multiple types of customers. The difference between customers' types is defined by the offered rewards. We show that the optimal admission control policy for maximizing the long-run average reward per unit time has a trunk reservation structure. Meanwhile, if the equipment is off, there exists a threshold of the queue length, above which the optimal repair speed is increasing in the queue length and below which the optimal repair speed is 0.

Optimality of admission control in an M∕M∕1∕N queue with varying services

Motivated by communication networks, we study a single-server queue with varying service rates and multiple customers’ types. The difference between types of customers is defined by the profits contributed to the system. We show that the optimal trunk reservation policy exists and we compare the optimal control levels with different parameter values. Furthermore, when the optimal trunk reservation policy is more than one, we prove the uniqueness of the bias optimal policy.

Bias optimality of admission control in a non-stationary repairable queue

We study a non-stationary repairable queue with a single server and multiple customers’ types. The difference between types of customers is defined by the offered rewards. We show that the bias optimal policy has the trunk reservation (threshold) form. Furthermore, under some given conditions, we also prove that the control level of the bias optimal policy is monotone about time.

Inter-Routes Fairness Strategies Inspired by Trunk Reservation Technique

Elastic Optical Network (EON) has emerged as a solution to manage different kinds of services, improving network scalability and efficiency. However, EONs tend to present differences in service performance due to the uneven bandwidth requirements. In addition, uneven network performance among routes with different hop counts is a known issue, affecting not only optical networks or EONs, but also computer networks. We call this problem inter-routes unfairness. In this letter we propose strategies based on the trunk reservation technique to solve it. Our results show that it is possible to deal with the inter-routes unfairness problem. We believe that this kind of strategy opens opportunities to be applied for connections traveling longer and more loaded routes, that would lead to a minimum impact in the overall network performance.

Optimal strategies for managing complex authentication systems

We study an authentication system that receives requests from different types of users. A centralized controller must assign an authentication method to each request, considering the type, the state of the system and the characteristics of several available methods. Each authentication method has different capacity, service rate, level of security, level of usability and operating cost. We seek to optimize security, usability and operating cost, simultaneously by assigning authentication methods dynamically, in real time. To do this, we model the system as a network of parallel multi-server queues, where each queue represents an authentication method and each customer represents a request. We use two different approaches to handle the multiple objectives: a weighted total cost function, and treating security and latency as constraints while minimizing operating cost. We employ constrained and unconstrained Markov decision processes to determine the structure of policies that effectively balance these three objectives. We conclude that if there are infinitely many servers for each authentication method, then the optimal policy is static. We also show that if one method has finite capacity, then the optimal policy is of trunk reservation form. Our results regarding the structure of the optimal policy are consistent for both modeling approaches. Our work shows that optimal policies have intuitive, easy-to-implement structures that are useful in practice. Under certain assumptions, we provide a straightforward way to obtain an optimal policy. We also offer strategies to use our models to explore non-dominated solutions over the three objective functions.

Optimality of admission control in a repairable queue

We study a repairable M∕M∕1∕N queueing system with multiple types of customers. The difference between customers’ types is defined by the offered rewards. Once customers are admitted to the system, they have the same service rate. We show that under the average reward criterion, all optimal (deterministic) stationary policies have the trunk reservation form. We then prove the uniqueness of the bias optimal policy.

Performance of a trunk reservation policy in distributed data centres

In this paper, we analyse a system composed of two data centres with limited capacity in terms of computing (namely virtual cores). When one request for a single core is blocked at the first data centre, this request is forwarded to the second one. To protect the requests originally assigned to the second data centre, a trunk reservation policy is introduced (i.e., a redirected request is accepted only if the number of free cores at the second data centre is greater than a given threshold). After rescaling the system when there are many cores in both data centres and high request arrival rates, we are led to analyse a random walk in the quarter plane, which has the particularity of having nonconstant reflecting conditions on one boundary of the quarter plane. Computing the stationary distribution of the present random walk requires the determination of three unknown functions, one polynomial and two infinite generating functions. We show that the coefficients of the polynomial are solutions to a linear system. After numerically solving this linear system, we are able to compute the two other unknown functions and the blocking probabilities at both data centres. Numerical experiments are eventually performed to estimate the gain achieved by the trunk reservation policy.

Overflow models for the admission of intensive care patients.

An earlier article, inspired by overflow models in telecommunication systems with multiple streams of telephone calls, proposed a new analytical model for a network of intensive care units (ICUs), and a new patient referral policy for such networks to reduce the blocking probability of external emergency patients without degrading the quality of service (QoS) of canceled elective operations, due to the more efficient use of ICU capacity overall. In this work, we use additional concepts and insights from traditional teletraffic theory, including resource sharing, trunk reservation, and mutual overflow, to design a new patient referral policy to further improve ICU network efficiency. Numerical results based on the analytical model demonstrate that our proposed policy can achieve a higher acceptance level than the original policy with a smaller number of beds, resulting in improved service for all patients. In particular, our proposed policy can always achieve much lower blocking probabilities for external emergency patients while still providing sufficient service for internal emergency and elective patients. In addition, we provide new accurate and computationally efficient analytical approximations for QoS evaluation of ICU networks using our proposed policy. We demonstrate numerically that our new approximation method yields more accurate, robust and conservative results overall than the traditional approximation. Finally, we demonstrate how our proposed approximation method can be applied to solve resource planning and optimization problems for ICU networks in a scalable and computationally efficient manner.

Threshold Relaxation and Holding Time Limitation Method for Accepting More General Calls under Emergency Trunk Reservation

Threshold Relaxation and Holding Time Limitation Method for Accepting More General Calls under Emergency Trunk Reservation

Selective Trunk with Multiserver Reservation

We consider a queueing model that is primarily applicable to traffic control in communication networks that use the Selective Trunk Reservation technique. Specifically, consider two traffic streams competing for service at ann-server queueing system. Jobs from theprotectedstream, stream 1, are blocked only if allnservers are busy. Jobs from thebest effortstream, stream 2, are blocked ifn-r, r≥1, servers are busy. Blocked jobs are diverted to a secondary group ofc-nservers with, possibly, a different service rate. We extend the literature that studied this system for the special case ofr=1and present an explicit computational scheme to calculate the joint probabilities of the number of primary and secondary busy servers and related performance measures. We also argue that the model can be useful for bed allocation in a hospital.

Trunk Reservation for Fair Utilization in Flexible Optical Networks

Flexible optical network (FON) architectures are considered a very promising solution where spectrum resources are allocated within flexible frequency grids. These architectures must handle the spectrum more efficiently and must support on-demand elastic bandwidth provisioning. However, when multi-bandwidth services coexist without a suitable bandwidth management, blocking of wider spectrum calls increases compared to narrower spectrum calls. This unfairness effect limits FONs' performance, not fulfilling much of the promise they hold. In this letter we present a new specific variant of trunk reservation policies that can effectively deal with fast on-demand bandwidth provisioning. Through network simulations we show that trunk reservation is able to guarantee fairness and to equalize the performance of an entire network in terms of blocking probability and link utilization with different flexible spectrum allocation policies.

Performance Analysis of Circuit Switched Multi-Service Multi-Rate Networks With Alternative Routing

We consider a circuit-switched multiservice network with non-hierarchical alternative routing and trunk reservation. Based on the fundamental concept of overflow priority classification approximation (OPCA), we develop two approximations for the estimation of the blocking probability: OPCA and service-based OPCA. We also apply the classical Erlang fixed-point approximation (EFPA) for the estimation of the blocking probability in the network and propose the more conservative max (EFPA, service-based OPCA) as a reasonably accurate evaluation. We compare the approximations with simulation results and discuss the accuracy of the blocking probabilities for the various traffic classes under different system parameter values such as service rates, bandwidth requirements, number of channels per trunk, maximum allowable number of alternative paths and trunk reservation. We also discuss the robustness of the approximations to the shape of the holding time distribution and their performances under asymmetrical cases. We illustrate that when the approximations are used for network dimensioning, their error is acceptable. We further demonstrate that the approximations can be applied in large networks such as the CORONET.

Blocking Probability Analysis of Circuit-Switched Networks With Long-Lived and Short-Lived Connections

We consider a circuit-switched network with nonhierarchical alternate routing and trunk reservation involving two types of connections that are modeled as long-lived and short-lived calls. The long-lived calls can be reserved well in advance, and the short-lived calls are provided on demand. Therefore, we assume that the long-lived calls have strict priority over the short-lived ones. We develop approximations for the estimation of the blocking probability based on the quasi-stationary approach in two ways. One uses the Erlang fixed-point approximation (EFPA), and the other uses the overflow priority classification approximation (OPCA). We compare the results of the approximations with simulation results and discuss the accuracy of the approximations under different system parameters, such as ratio of offered load, number of links per trunk, maximum allowable number of deflections, and trunk reservation. We also discuss the robustness of the quasi-stationary approximation to the ratio of the mean holding times of the long-lived and short-lived calls as well as that of EFPA and OPCA to the shape of the holding time distribution. Finally, we demonstrate that OPCA can be applied to a large network such as the Coronet.

Optimal patient and personnel scheduling policies for care-at-home service facilities

In this paper we study the problem of personnel planning in care-at-home facilities. We model the system as a Markov decision process, which leads to a high-dimensional control problem. We study monotonicity properties of the system and derive structural results for the optimal policy. Based on these insights, we propose a trunk reservation heuristic to control the system. We provide numerical evidence that the heuristic yields close to optimal performance, and scales well for large problem instances.

OPTIMALITY OF TRUNK RESERVATION FOR AN M/M/K/N QUEUE WITH SEVERAL CUSTOMER TYPES AND HOLDING COSTS

In this article we study optimal admission to an M/M/k/N queue with several customer types. The reward structure consists of revenues collected from admitted customers and holding costs, both of which depend on customer types. This article studies average rewards per unit time and describes the structures of stationary optimal, canonical, bias optimal, and Blackwell optimal policies. Similar to the case without holding costs, bias optimal and Blackwell optimal policies are unique, coincide, and have a trunk reservation form with the largest optimal control level for each customer type. Problems with one holding cost rate have been studied previously in the literature.

A new convolution algorithm for loss probability analysis in multiservice networks

Performance analysis in multiservice loss systems generally focuses on accurate and efficient calculation methods for traffic loss probability. Convolution algorithm is one of the existing efficient numerical methods. Exact loss probabilities are obtainable from the convolution algorithm in systems where the bandwidth is fully shared by all traffic classes; but not available for systems with trunk reservation, i.e. part of the bandwidth is reserved for a special class of traffic. A proposal known as asymmetric convolution algorithm (ACA) has been made to overcome the deficiency of the convolution algorithm. It obtains an approximation of the channel occupancy distribution in multiservice systems with trunk reservation. However, the ACA approximation is only accurate with two traffic flows; increased approximation errors are observed for systems with three or more traffic flows. In this paper, we present a new Permutational Convolution Algorithm (PCA) for loss probability approximation in multiservice systems with trunk reservation. This method extends the application of the convolution algorithm and overcomes the problems of approximation accuracy in systems with a large number of traffic flows. It is verified that the loss probabilities obtained by PCA are very close to the exact solutions obtained by Markov chain models, and the accuracy outperforms the ACA approximation.

Optimal trunk reservation for an overloaded link

We consider a single overloaded link with a large number of circuits which is offered two kinds of calls. The traffic intensity of the primary calls is assumed to be strictly less than 1, and R of the circuits are reserved for these. Rewards are generated when calls are accepted, and it is assumed that the reward for primary calls is greater than that for secondary calls. We determine the trunk reservation parameter R which asymptotically maximizes the long run average reward.

A New Method for Blocking Probability Evaluation in OBS/OPS Networks With Deflection Routing

In this paper, we present a new method for the estimation of blocking probabilities in bufferless optical burst or packet switched networks. In such networks, deflection routing is used to reduce blocking probability. However, it requires certain wastage due to trunk reservation that must be used to avoid instability. We provide a wide range of simulation and numerical results to validate our new approximation method and demonstrate various effects on blocking probability and utilization, such as network size, trunk size, the maximal number of allowable deflections, and burst/packet length.

Asymptotic Analysis of a Loss Model with Trunk Reservation II: Trunks Reserved for Slow Traffic

We consider a model for a single link in a circuit switched network. The link has C circuits, and the input consists of offered calls of two types, that we call primary and secondary traffic. Of the C links R are reserved for primary traffic. We assume that both traffic types arrive as Poisson arrival streams. Assuming that C is large and R=O(1), the arrival rate of secondary traffic is O(C) while that of primary traffic is smaller, of the order . The holding times of the secondary calls are assumed exponentially distributed with unit mean. Those of the primary calls are exponentially distributed with a large mean, that is . The loads for both traffic types are thus comparable (O(C)) and we assume that the system is “critically loaded,” i.e., the system's capacity is approximately equal to the total load. We analyze asymptotically the steady state probability that n2 (resp. n1) circuits are occupied by primary (resp. secondary) calls. In particular, we obtain two‐term asymptotic approximations to the blocking probabilities for both traffic types. This work complements part I, where we assumed that the secondary traffic had an arrival rate that was and a service rate that was . Thus in part I the R trunks were reserved for the “fast traffic,” whose arrival and service rates were O(C) and O(1).