Performance analysis of polling systems with retrials and glue periods

We consider gated polling systems with two special features: (i) retrials, and (ii) glue or reservation periods. When a type-$i$ customer arrives, or retries, during a glue period of station $i$, it will be served in the next visit period of the server to that station. Customers arriving at station $i$ in any other period join the orbit of that station and retry after an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. For the case of exponentially distributed glue periods, we present an algorithm to obtain the moments of the number of customers in each station. For generally distributed glue periods, we consider the distribution of the total workload in the system, using it to derive a pseudo conservation law which in its turn is used to obtain accurate approximations of the individual mean waiting times. We also consider the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times

Size-based routing to balance performance of the queues

\u3cp\u3eWe study a queueing system with a Poisson arrival process, in which a dispatcher sends the jobs to K homogeneous queues. The dispatcher knows the size of each job, and can implement a size-aware policy. Instead of trying to optimize system performance, we propose a Size Interval Task Assignment (SITA) policy that aims to equalize the performance (mean waiting times, or mean queue lengths) of all queues by allocating the jobs to the queues according to size. Such SITA routing requires no communication between the servers and the dispatcher, and is hence easily implemented. We study existence and uniqueness of the allocation thresholds. For FCFS and PS queues in heavy traffic, those thresholds coincide with those of a dispatching rule, SITA-E, in which loads are balanced. Preliminary numerical studies suggest that a SITA dispatching policy that equalizes performance is close to optimal when the difference between the size of the largest and the smallest job is small.\u3c/p\u3

Performance analysis of polling systems with retrials and glue periods

Abstract\u3cbr/\u3e\u3cbr/\u3eWe consider gated polling systems with two special features: (i) retrials and (ii) glue or reservation periods. When a type-i customer arrives, or retries, during a glue period of the station i, it will be served in the following service period of that station. Customers arriving at station i in any other period join the orbit of that station and will retry after an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. When the glue periods are exponentially distributed, we obtain equations for the joint generating functions of the number of customers in each station. We also present an algorithm to obtain the moments of the number of customers in each station. When the glue periods are generally distributed, we consider the distribution of the total workload in the system, using it to derive a pseudo-conservation law which in turn is used to obtain accurate approximations of the individual mean waiting times. We also investigate the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times.\u3cbr/\u3

Revenue maximization in an optical router node : allocation of service windows

\u3cp\u3eIn this paper we study a revenue maximization problem for optical routing nodes. We model the routing node as a single server polling model with the aim to assign visit periods (service windows) to the different stations (ports) such that the mean profit per cycle is maximized. Under reasonable assumptions regarding retrial and dropping probabilities of packets the optimization problem becomes a separable concave resource allocation problem, which can be solved using existing algorithms.\u3c/p\u3

Revenue maximization in an optical router node using multiple wavelengths

In this paper, an optical router node with multiple wavelengths is considered. We introduce revenue for successful transmission and study the ensuing revenue maximization problem. We present an efficient and accurate heuristic procedure for solving the NP-hard revenue maximization problem and investigate the advantage offered by having multiple wavelengths

Revenue maximization in an optical router node using multiple wavelengths

\u3cp\u3e In this paper, an optical router node with multiple wavelengths is considered. It is assumed that successful transmission of a packet of type j at station (= port) i of the router node gives a profit γij, but that there is also a positive probability that such a packet is dropped, causing a penalty θ \u3csub\u3eij\u3c/sub\u3e . This brings us to the formulation of a revenue optimization problem. Consider one fixed cycle, in which each station is assigned some visit time at one of the wavelengths. We aim to maximize the revenue by optimally assigning stations to wavelengths and, for each wavelength, by optimally choosing the visit times of the allocated stations within the cycle. This gives rise to a mixed integer linear programming problem (MILP) which is NP-hard. To solve this problem fast and efficiently we provide a three-step heuristic. It consists of (i) solving a separable concave optimization problem, then (ii) allocating the stations to wavelengths using a simple bin packing algorithm, and finally (iii) solving another set of separable concave optimization problems. We present numerical results to investigate the effectiveness of the heuristic and the advantages of having multiple wavelengths. \u3c/p\u3