Justice HOBBS

delivered the Opinion of the Court.

We issued a rule to show cause in this original proceeding under C.A.R. 21 to review whether Robert Ward Bullard (Bullard), an inmate at the Bent County Correctional Facility, is entitled to issuance of a writ of mandamus ordering his discharge from the custody of the Department of Corrections (DOC). At issue are two sentences of two district courts in separate cases involving judgments of conviction against Bullard. The Montrose County District Court issued an order on June 2, 1997, directing the DOC to discharge Bullard from custody because his sentence, including the mandatory parole period, had been served. DOC responded to our rule and argues that the Montrose court lacked jurisdiction to eliminate Bullard’s mandatory parole term and, in the alternative, if the order was valid, that Bullard is in lawful DOC custody because he is serving a parole term for an El Paso County District Court conviction. We recognize the validity of the Montrose order declaring Bullard’s sentence complete in ease number 95CR31, and we make the rule absolute as to the Montrose sentence. However, we discharge the rule in case number 95CR0369 because Bullard has not demonstrated completion of the El Paso sentence.

The Montrose district court on May 3, 1995, sentenced Bullard to two years in DOC custody after he pled guilty to a charge of Conspiracy to Commit Second Degree Burglary, a class 5 felony. A mandatory two year parole period accompanies this offense. See § 18-l-105(l)(a)(V)(A), 6 C.R.S. (1997).

On June 2, 1995, the El Paso County District Court sentenced Bullard to eighteen months in DOC custody after he entered a guilty plea to a charge of Habitual Offender — Driving on Revoked License, a class 5 felony, which also carries a mandatory two year parole period. See § 18-1-105. The El Paso court ordered its sentence to run concurrently with the Montrose court’s sentence:

It is the judgment of this Court that the Defendant be sentenced to: THE DEPARTMENT OF CORRECTIONS, FOR A TERM OF 18 MONTHS, CONCURRENT WITH MONTROSE COUNTY CASE # 95CR0031, and subject to all regulations of that department.

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THEREFORE IT IS ORDERED: The Sheriff of El Paso County shall convey the Defendant to be received and kept as provided by law.

Bullard received fifty-four days of credit for presentence confinement and 170 days of earned time credit towards his Montrose sentence. On September 19, 1996, DOC released him to serve his two year parole term. In addition to his credits, he had served one year, four months and sixteen days of the Montrose sentence. As of his release date, Bullard had also served one year, three months, and seventeen days of his El Paso sentence, which commenced on June 2, 1995. On October 21, 1996, the Colorado State Board of Parole revoked Bullard’s parole.

On June 2, 1997, Bullard petitioned the Montrose court for a corrected sentence and argued that he had pled guilty in exchange for a total of two years in prison. The Montrose court declared that the sentence in case number 95CR31 was for “a two year stipulated sentence inclusive of parole” and found that the sentence had been served— “including any parole period” — and that Bul-lard should be discharged from DOC custody. Bullard served the prosecution with his “Motion to Correct Sentence.” The people did not file a brief in opposition or appeal the Montrose court’s discharge order.

Despite the Montrose order, the DOC did not discharge Bullard. DOC argues' that the Montrose order is void and that Bullard has time remaining on that sentence. Bullard now seeks mandamus through an original proceeding claiming a violation of the Mont- *1001 rose discharge order which Bullard claims entitles him to discharge on the El Paso sentence as well. We issued a rule in both the Montrose and the El Paso cases directing DOC to show cause why Bullard should not be released from DOC custody. 1

In his pro se motion, Bullard argues that the sentence imposed by the El Paso district court was to conform in all respects to that imposed by the Montrose district court and, thus, he is entitled to be discharged from incarceration. DOC responds that the El Paso sentence has not been completed and that Bullard’s discharge date is September 19, 1998, because of the parole revocation. Bullard has not presented us with any order of the El Paso court regarding relief as to its judgment of conviction and sentence or made any showing that he has applied to that court for relief.

II.

In requesting mandamus relief, Bul-lard must satisfy a three-part test: (1) he must have a clear right to the relief sought; (2) the DOC must have a clear duty to perform the act requested; and (3) there must be no other available remedy. See Gramiger v. Crowley, 660 P.2d 1279, 1281 (Colo.1983). At issue is whether the Montrose order is void and, if not, whether the Montrose order also disposes of the sentence imposed by the El Paso district court. The Montrose order is a final order which was not appealed. It is valid and must be implemented by the DOC. It does not, however, dispose of the El Paso sentence.

In arguing that the Montrose order obligates the DOC to discharge him from custody, Bullard asserts that the longer, “controlling” Montrose sentence has been served; thus, the shorter, concurrent El Paso sentence has been served as well. DOC counters that, even if the Montrose order is valid, Bullard still must serve the statutory two year parole period for the El Paso conviction because the Montrose court lacked jurisdiction to modify the El Paso sentence. We agree, and refuse to issue a writ of mandamus ordering Bullard’s release from custody in regard to the El Paso sentence. However, we make the rule absolute in the Montrose case to enforce that court’s final order declaring Bullard’s Montrose sentence to have been completed and ordering his release as to that sentence.

The Montrose Case

DOC requests that we find the Montrose court’s order to be invalid because the court cannot disregard a sentencing statute or “ ‘interfere with the executive ... in the performance of its statutory duties’.” DOC “Response to Order to Show Cause” at 4-5 (quoting Kort v. Hufnagel, 729 P.2d 370, 373 (Colo.1986)).

Separation of powers “operates to prohibit the judiciary from preempting an executive agency from exercising powers properly within its own sphere.” Hufnagel, 729 P.2d at 373. The DOC is part of the executive branch and the executive’s function is “to see that the laws are faithfully executed.” State v. Pena, 911 P.2d 48, 55 (Colo.1996). In carrying out that function, the DOC is required by law to take custody of state-sentenced prisoners, see id., -including those prisoners whose parole terms have been revoked. See § 17-22.5-303(7), 6 C.R.S. (1997) (if parole is revoked, board of parole shall “order the return of the offender to the institution in which he was originally received”). This court has held that ‘“for the limited purpose of taking custody of prisoners as directed by the mittimus’,” DOC officials are “ ‘officers of the court’.” Pena, 911 P.2d at 56 (quoting People v. Lockhart, 699 P.2d 1332, 1336 (Colo.1985)).

When a prisoner’s sentence has been served, or when a sentence has been declared completed by a final and effective court ruling, the DOC must obey a judicial order for discharge that is not subject to appeal. While this court has acknowledged that a trial court may lack the authority to “super *1002 vise” an executive agency, we have also noted that where an executive officer fails to comply with a final order of a trial court, such court “may take appropriate steps to enforce, its order.” Pena, 911 P.2d at 56. Without this power, the role of the courts as a separate and independent branch of government would be meaningless. For example, if the courts could not enforce the sentences they impose by directing the DOC to take custody of prisoners, the courts’ power and duty to order punishment of convicted criminals would be ineffectual. See id.

In Colorado, sentencing is predominantly a matter of discretion with the trial court. People v. District Court, 673 P.2d 991, 995 (Colo.1983). Here, upon review of the facts of < its case, the Montrose court declared the sentence it imposed to have been completed in accordance with a plea agreement made by the state for a total of two years in prison. Its order clearly states that Bullard’s sentence “is hereby deemed completed including any parole period.” (Emphasis added.)

The Montrose court had the authority to review the circumstances of Bullard’s plea agreement and sentence in case number 95CR31. See, e.g., St. James v. People, 948 P.2d 1028, 1032 (Colo.1997) (plea agreement is subject to enforcement by trial court); People v. McCormick, 859 P.2d 846, 858 (Colo.1993) (determination of breach of plea agreement is question for trial court). The state chose not to appeal the court’s order. Thus, the order for release as to case number 95CR31 is final and effective.

In the absence of an appeal, we do not reach the propriety of the district court’s application of the Sandoval case to Bullard’s plea agreement. See People v. Sandoval, 809 P.2d 1058 (Colo.App.1990) (where mandatory parole term added time to sentence defendant bargained for, court should have informed defendant before accepting plea, and remedy was to reduce sentence to conform with maximum that defendant bargained for). The Montrose court construed its sentence as imposing no incarceration and two years of mandatory parole in order to avoid a sentence which illegally ignored the statutory parole period. While the parole period in section 18-l-105(l)(a)(V)(A) is mandatory, the minimum and maximum sentences are “presumptive ■ ranges.” § 18-1-105(l)(a)(V)(A), 6 C.R.S. (1997).

The El Paso Case

The DOC contends that, even if the Mont-rose order is given effect, Bullard cannot be discharged because he has not completed his El Paso sentence. We agree. The Montrose court did not address the circumstances of the El Paso plea bargain, judgment of conviction, and court sentence, nor did it have the authority to do so. We have not been presented with any order of the El Paso district court either granting or failing to grant relief to Bullard with regard to that courtfs judgment of conviction and sentence.

The El Paso court ordered its sentence to run concurrently with the Montrose sentence. “A concurrent sentence is one which runs simultaneously, in whole or in part, with another sentence.” Brinklow v. Riveland, 773 P.2d 517, 520 (Colo.1989). Bullard argues that the Montrose sentence is the “controlling” sentence, as well as the longer sentence, and, if it is complete, the El Paso sentence must be as well. Bullard’s understanding of concurrent sentences is mistaken. When two sentences run concurrently, it merely means that, for each day in custody while serving both sentences, the inmate receives credit toward each sentence. Concurrent sentences do not necessarily begin and end at the same time — they simply run together during the time that they overlap. Id. (citing 24B C.J.S. Criminal Law § 1996(1) (1962)).

The El Paso judgment of conviction clearly states that Bullard is sentenced to the DOC “for a term of 18 months, concurrent with Montrose County case # 95CR0031, and subject to all regulations of that department.” Once the Montrose court had reviewed its sentence in light of the plea bargain in that court, the El Paso sentence became the longer of the two: eighteen months of incarceration plus two years of mandatory parole under the applicable stat *1003 ute, the remainder of which must now be served in DOC custody because of the parole revocation and applicable DOC regulations. See § 17-22.5-303(7), 6 C.R.S. (1997).

The Montrose court had no authority to construe or terminate the El Paso sentence; nor, despite Bullard’s wish to the contrary, do we perceive that the Montrose court attempted to do so. “[T]ermination of his first sentence had no effect on the unserved portion of his second sentence.” Brinklow, 773 P.2d at 520 (Denver district court’s finding that defendant’s sentence had been served and order for his discharge did not affect concurrent Teller County sentence).

Bullard became eligible for parole in the El Paso ease on the same date as- in the Montrose case — September 19, 1996 — after serving one year, three months and seventeen days of the El Paso sentence. His parole was subsequently revoked; Bullard did not contest that revocation nor has he sought relief from the El Paso court similar to the relief which he requested of the Mont-rose court. Bullard’s two year mandatory parole extends to September 19, 1998, and must now be served in DOC custody because of the revocation.

It is apparent that Bullard has not satisfied the three part test for mandamus relief as to the outstanding El Paso sentence. See Gramiger v. Crowley, 660 P.2d 1279, 1281 (Colo.1983). First, he has not established a clear right to the relief sought because he has not demonstrated that the El Paso sentence has been served. Second, he has not proven that the DOC has a clear duty to release him; because his parole was revoked, the DOC is required to keep him in custody. Finally, another remedy appears to be available to Bullard — he could ask the El Paso court to review that court’s sentence and grant appropriate relief.

III.

Because Bullard has not established his right to be released from DOC custody with regard to the El Paso sentence, we cannot issue a writ of mandamus directing his discharge from incarceration. Thus, we discharge the rule to show cátise issued in case number 95CR0369. We make the rule absolute in case number 95CR31. Accordingly, while we require the DOC to release Bullard as to the Montrose sentence, we do not order Bullard released as to the El Paso sentence because he has not demonstrated- completion of the mandatory two year parolé period prescribed by statute for the El Paso offense.

. Bullard has moved the Montrose district court to issue an order to show cause why the DOC is not in contempt for failing to comply with the court’s order. The Montrose court has appropriately declined to act on this motion pending our decision in this original proceeding.