Abstract: The binomial queue, a new data structure for implementing priority queues that can be efficiently merged, was recently discovered by Jean Vuillemin; we explore the properties of this structure in d...

Abstract: A queuing system with a buffer of unlimited capacity in front of a cyclic arrangement of two exponential server queues is analyzed. The main feature of the system is blocking, i.e., when the population in the two queues attains a maximum value M, say, new arrivals are held back in the buffer. The solution is given in form of polynomial equations which require the roots of a characteristic equation. A solution algorithm is provided. The stability condition is given in terms of these roots and also in explicit form. Limiting cases which are of practical interest are discussed. These limiting cases lead to a better understanding of some popular approximation techniques.

Abstract: Queues with autonomous service (QAS) represent service systems in which the server becomes unavailable for a random time after each service epoch. Such systems have been used to model secondary memory devices in computer systems (e.g. paging disks or drums). The queue with server of walking type studied by Skinner [1] is a special instance of our model. This model has also been considered by Borovkov [2]. Assuming general independent interarrival times we obtain an operational formula relating the waiting time in stationary state of a QAS to the waiting time of a GI/G/l queue. This result dispenses the need for analysis of the QAS in special cases and generalizes the result of Skinner [1], or that of Coffman [3] for a paging drum. Sufficient conditions for stability or instability of the system are also obtained.

Abstract: Obtaining time dependent results for many server queues is, under general structural assumptions, a hard problem. This paper makes an attempt to approximate stochastically the behaviour of a general many server queue by using single server queues as stochastic bounds. We propose three alternative ways of constructing approximating single server queues. The first technique utilizes special classes of service time distributions new better than used, new worse than used, the second is via dividing the service times by the number of servers, and the third is based on a grouping idea of the customers. The first and third techniques yield in fact two bounding queues each, one of which is faster and one slower than the original s-server queue.

Abstract: We consider an exponential queuing system consisting of several removable servers in which the arrival rate depends on the current system state. Costs are incurred at a rate that depends on both the number of customers present and the number of servers in operation. We present conditions that ensure that the number of servers in operation is a non-decreasing function of the number of customers in the system.

Abstract: Concentrating rooted tree networks of discrete-time single server queues, all with unit service time, are considered. Such networks occur as subnetworks connecting remote access terminals to a node in a data communications network. It is shown that the network of queues may be replaced by a single queue, with prescribed input, which has the same output as the queue at the root of the tree. The result is applied, in particular, to the case of several queues in tandem, and it is shown how this problem may be reduced to that of just two queues in tandem. The latter problem was analyzed earlier by the author.

Abstract: We consider the problem of optimally controlling a semi-Markov chain with countable state space and unbounded costs. We assume that a particular control is suspected of being optimal and derive conditions for checking whether this is so. The result is applied to the following queueing system. A single server serves two types of customers who arrive at random and join separate queues. The two types of customer differ in respect of their arrival rates, waiting costs and service time distributions. The server has control over which queue to serve at any time and may interrupt the service of a customer in order to serve a customer of the other queue. In the latter case, however, an interruption cost is incurred which reflects the disruption or loss of goodwill entailed. The server requires a policy for determining when he should switch queues which minimises the long run expected cost per unit time. We find that such a policy specifies that one of the queues has higher priority. When the service time distribution of the other queue is exponential, this priority is pre-emptive if the length of the higher priority queue exceeds a critical value and is otherwise postponable. When the distribution is Erlang-2, the priority depends both on the length of the priority queue and the phase of service.

Abstract: Several control schemes have been proposed in the past for optimal control of congested intersections but they have not been applied in real life situations partly because of the complex instrumentation required for their application and partly because they do not combine all control objectives at such intersections. Open and closed loop control policies minimizing total intersection delays subject to queue size constraints have also been proposed by the authors. All control policies, however, have the disadvantage that they are based on simple traffic models describing the effective size of the queues rather than the queue lengths. In this paper a new model is presented describing the queue dynamics at signalized intersections as a function of the demands, the intersection characteristics and the control decisions. A control policy combining the results of this model and control principles previously developed by the authors is also proposed.

Abstract: To decide on the queuing system of the optimum-sized bank window, data by means of simulation was reckoned. That is, by linking the average arrival rate and the average service rate with the exponential random number, customers' arrival time and service time was reckoned and simulation size optionally decided. By so doing, this paper is aimed at predicting the conditions of a bank, average arrival time, average waiting time, average service time, average queuing length, servers' idle time, etd, and at preparing for a simulation model of the queuing system that can apply not only to the bank window box but also to all system under which queuing phenomena may arise.

Abstract: We consider a queuing system with several identical servers, each with its own queue. Identical customers arrive according to some stochastic process and as each customer arrives it must be assigned to some server's queue. No jockeying amongst the queues is allowed. We are interested in assigning the arriving customers so as to maximize the number of customers which complete their service by a certain time. If each customer's service time is a random variable with a non-decreasing hazard rate then the strategy which does this is one which assigns each arrival to the shortest queue.