Consider a two-server, ordered entry, queuing system with heterogeneous servers and finite waiting rooms in front of the servers. Service times are negative exponentially distributed. The arrival process is deterministic. A matrix solution for the steady state probabilities of the number of customers in the system is derived. The overflow probability will be used to formulate the stability condition of a closed-loop conveyor system with two work stations.
Consider a single server loss system in which the server, being idle, may reject or accept an arriving customer for service depending on the state at the arrival epoch. It is assumed that at every arrival epoch the server knows the service time of the arriving customer, the arrival time of the next customer and the service time. The server gets a fixed reward for every customer admitted to the system. The form of an optimal stationary policy is investigated for the discounted and average reward cases.
Consider a many-server queueing system in which the servers are numbered. If a customer arrives when two or more servers are idle he selects the server with lowest index (this is called the ordered entry selection rule). An explicit expression for the traffic handled by the various servers in a GI/M/s queueing system with ordered entry is derived. For the M/M/s queueing system the probability distribution of the number of busy servers among the first k(k = 1,2, ---, s) servers will be given. Finally, a formula for the traffic handled by the first server in an MID/s system will be derived. All results are derived under steady-state conditions. As an application some numerical data for the server utilizations will be given and compared to data obtained from simulation studies of a closed-loop continuous belt-conveyor.
This paper considers a service system with a single server, finite waiting room, and a renewal arrival process. Customers who arrive while the server is busy are lost. Upon completing service, the server chooses between two actions: either he immediately starts a new service, provided a customer is present, or he admits the newly arrived customer to the system, but delays service pending the next arrival, whereupon he again chooses between these two actions. This process continues until either the system is full or a new service is started. Once a service has been started, all customers who arrive while the server is busy are lost. We assume that at each decision epoch the server knows the arrival epoch of the first arriving customer. We show that there exists an optimal control-limit policy that minimizes the average expected idle time per customer served (equivalently, maximizes the average number of customers served per unit of time). The special case of Poisson arrivals leads to an explicit expression for this delay that generalizes exisiting results.T HE MODEL considered in this paper originates from the following problem. Consider a work station, situated along a conveyor, comprised of a storage buffer of finite capacity and a machine served by an operator. Since the operator unloads the parts arriving on the conveyor and also performs the necessary operations on the parts, parts arriving during a service are lost. If the operator can always see the first oncoming part, the question arises as to which unloading policy will maximize the production rate of the work station.Our model is a service system with one server and finite waiting room. Customers arrive according to an ordinary renewal process. Upon terminating a service, the server notes the time that elapses until the next arrival. We assume that he immediately detects this time with certainty. Having observed this time, the server can choose between two actions: either instantaneously start a new service, provided a customer is present, or delay service until the next arrival and admit the newly arriving customer to the system. In the latter case he notes the arrival epoch of the subsequent customer, which has just become known to him, and Subject classification: 119 look-ahead policy for admission to single server system, 587 unloading policy for conveyor-serviced work station, 601 admission control to single server queue.
This paper gives a queuing analysis of a conveyor-serviced production station using a state-dependent sequential range policy for unloading units from the conveyor into a reserve. The stationary distribution of the number of units in the reserve and the expected delay per unit processed are derived for a Poisson arrival process. The f~rm of the optimal unloading policy, which minimizes the expected delay, will be established.
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